5 6 slideand_divide_11_19_12
Download as ppt, pdf0 likes212 views
This document provides examples and steps for factoring trinomials using the "slide and divide" method. It demonstrates factoring trinomials of the form ax^2 + bx + c through 4 examples, showing the steps of finding the greatest common factor, "sliding" terms to group like terms, factoring, dividing and simplifying, and "pushing back" the factors. Exercises are assigned from the green algebra book problems 25-39 odds on page 328.
1 of 7
Download to read offline
Ad
Recommended
Taller matem叩ticas empresariales.
Taller matem叩ticas empresariales.Daniela V辿lez
油
The document provides 18 math equations involving variables like x, y, m, r, a, and c. The equations include operations like addition, subtraction, multiplication, exponents, and grouping terms using parentheses. For example, one equation is (x-2y)2 + 2(x-2y)(z-3r) + (z-3r)2, another is 4m10 + 4m7 - m4 - m8 - 1. The document presents the equations without context or explanation of the variables.Day 3 subtracting polynomials
Day 3 subtracting polynomialsErik Tjersland
油
This document provides examples and instructions for subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing common terms and combining like terms, such as (3x^2 + x + 2) - (2x^2 - x + 3). The document ends with homework assignments involving subtracting various polynomials.Module 10 Topic 3 factoring perfect square & difference of square
Module 10 Topic 3 factoring perfect square & difference of squareLori Rapp
油
This document provides instruction on factoring perfect square trinomials and the difference of squares. It includes links to video explanations of factoring perfect square trinomials. It provides examples of factoring a perfect square trinomial and the difference of squares, including splitting the perfect square and finding the difference. Students are instructed to practice these skills on interactive math websites and problems, and to complete an assessment with multiple choice questions in an online factoring Gizmo simulation.Aptitude 30 questions paper
Aptitude 30 questions paperpuneet8589
油
The document contains 30 questions on various technical topics including programming languages like Java, C, PL/SQL and databases. It also includes questions on logic, math, probabilities and algorithms. The questions range from basic to advanced levels and cover a wide variety of concepts related to coding, databases, data structures and other computer science topics. The document serves as a sample for an aptitude test containing technical questions.8-5 Adding and Subtracting Rational Expressions
8-5 Adding and Subtracting Rational Expressionsrfrettig
油
1) Rational functions can be added or subtracted if they have a common denominator. To find the least common denominator (LCD), multiply the individual denominators together and divide by their greatest common factor (GCF).
2) Examples are provided of finding the LCD of rational expressions and adding or subtracting rational expressions after finding the LCD. Factoring is used to find the LCD.
3) The document provides examples of adding, subtracting, and simplifying rational expressions by finding the LCD and distributing terms in the numerators. Practice problems are assigned from the textbook.Divisors quotients and remainders
Divisors quotients and remaindersShaun Wilson
油
This document discusses division of polynomials. It explains that division is the opposite of multiplication and involves calculating a quotient and remainder. It shows examples of dividing numbers and polynomials, identifying the divisor, quotient, and remainder. It also introduces the "Big L" method for polynomial long division, which involves arranging the terms in a particular way to calculate the quotient and remainder.8.4 mixed.ppt worked
8.4 mixed.ppt workedJonna Ramsey
油
This document provides homework questions on identifying conic sections from their standard forms. It includes 8 equations of conic sections in standard form and asks the student to identify the conic, state important features, and graph each one. It reminds students they have a test on Monday and directs them to review problems on pages 698 of their textbook, problems 21-28 and 31-36.Day 11 factoring trinomials2
Day 11 factoring trinomials2Erik Tjersland
油
This document provides instructions on how to factor trinomials. It explains that to factor an expression of the form x^2 + bx + c, you need to find two numbers whose product is c and sum is b. It then provides examples of factoring various trinomial expressions like x^2 + 5x + 6 = (x + 2)(x + 3). At the end, it directs students to factor additional trinomials for homework.BBMP1103 - Sept 2011 exam workshop - part 7
BBMP1103 - Sept 2011 exam workshop - part 7Richard Ng
油
This document summarizes an exam preparation workshop on the application of partial differentiation presented by Dr. Richard Ng. It provides the answers to two sample exam questions, finding the critical points and determining whether they are maxima or minima for multivariate functions. For the first question, the critical point is found to be (7/3, 8/3) which is a minimum. For the second question, the critical point is (-4, 2) which is also determined to be a minimum using the second derivative test.BBMP1103 - Sept 2011 exam workshop - Part 2
BBMP1103 - Sept 2011 exam workshop - Part 2Richard Ng
油
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.Maximum and minimum
Maximum and minimumshirleyaporter
油
This document discusses using quadratic functions to find the minimum and maximum values without using much algebra. It shows that for the basic quadratic function y=x^2, the minimum value is found at x=0 and the minimum value is y=0. Adding a negative sign in front of x^2 inverts the graph, and the maximum value is found at x=0. Adding a constant inside the quadratic function slides the graph along the x-axis in the opposite direction of the constant.June 5, 2014
June 5, 2014khyps13
油
The document provides instruction on simplifying rational expressions and equations, including complex fractions. It reviews concepts like multiplication and division of rational expressions, addition and subtraction of rational expressions, finding the lowest common denominator, and working with complex fractions. Examples are provided to demonstrate these concepts and techniques for simplifying rational expressions and solving rational equations.Rational Inequality Apr 20 09
Rational Inequality Apr 20 09ingroy
油
The document discusses solving rational inequalities by:
1) Placing critical numbers on a number line
2) Solving the inequalities algebraically
3) Graphing the solutions on the number line between the critical numbers5 Polynomial Feb 18
5 Polynomial Feb 18mskarras
油
This document provides a summary of factoring techniques including:
1) Squaring binomials using the formula (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) Factoring the difference of squares using the formula (a2 - b2) = (a + b)(a - b).
3) Factoring trinomials that are the product of a sum and difference using the formulas a2 - b2 = (a + b)(a - b).
4) Cubing a binomial using the formula (a + b)3 = a3 + 3a2b5 Polynomial Feb 22
5 Polynomial Feb 22mskarras
油
This document provides a summary of factoring techniques including:
1) Squaring binomials using the formula (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) Factoring the difference of squares using the formula (a2 - b2) = (a + b)(a - b).
3) Factoring trinomials that are the product of a sum and difference using the formulas a2 - b2 = (a + b)(a - b).
4) Expanding cubes using the formula (x + a)3 = x3 + 3x2a +Divisi坦n de un polinomio entre un binomio
Divisi坦n de un polinomio entre un binomioprofesorluis
油
The document is a video cast that demonstrates dividing a polynomial by a binomial. It shows the step-by-step operations to divide the polynomial 5x^3 - 2x^2 + 3x + 1 by the binomial x + 1. The division results in the quotient of 5x^2 - 7x + 10 and the remainder of 0x - 9. The video cast provides credit to the source of an image and details about the software and music used.Day 11 factoring trinomials
Day 11 factoring trinomialsErik Tjersland
油
This document provides instructions for factoring trinomials using the method of finding two numbers whose product is the constant term and whose sum is the coefficient of the linear term. It includes examples of factoring various trinomials of the form x^2 + bx + c into the product of binomial factors (x + p)(x + q). The document aims to teach readers how to factor trinomials by finding the two numbers p and q that satisfy the given conditions.Day 3 subtracting polynomials
Day 3 subtracting polynomialsErik Tjersland
油
This document provides examples of subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing corresponding terms and using the opposite sign. For example, (3x^2 + x + 2) - (2x^2 - x + 3) is solved by removing the 2x^2 terms and changing the sign of the remaining terms to get x^2 + x - 1. It provides several more examples and problems for students to solve, including finding the area of a shaded region between a rectangle and square using polynomial subtraction.Topic 3 factoring perfect square & difference of square
Topic 3 factoring perfect square & difference of squareAnnie cox
油
This document provides instruction on factoring perfect square trinomials and difference of squares expressions. It includes links to video explanations of factoring perfect square trinomials. It provides examples of factoring a perfect square trinomial and difference of squares expressions, including step-by-step worked examples. Students are instructed to practice these skills using online factoring activities and games in order to correctly factor 4 out of 5 problems.Factoring trinomials
Factoring trinomialsguest7c2aac
油
This document provides instructions for factoring a trinomial. It gives the example of factoring x^2 + 7x - 18. The steps shown are writing out the trinomial, finding the greatest common factor of the first and last terms, then using that to write the trinomial as the product of two binomials, (x - 2)(x + 9), which provides the factored form of the original trinomial.C8 8.6
C8 8.6BGEsp1
油
This document contains 6 math word problems asking the reader to divide various polynomial expressions. Each problem is followed by the word "Solution" indicating the answer or worked out steps are to follow. The problems involve dividing expressions such as x^2 - 5x + 6 by x - 3, ax^2 - ay^2 by ax + ay, and (a^2 + 2ab + b^2) - (a^2 + 2ac + c^2) by 2a + b + c.Adding dissimilar fractions
Adding dissimilar fractionsNicko Salazar
油
The document shows steps to solve several fraction addition problems by finding a common denominator. It first shows 3814+ = n, finds the lowest common denominator of 8, and sets up the equivalent fractions with that denominator to solve. It then works through several more examples using the same process of finding the common denominator and setting up equivalent fractions to solve.Subtracting dissimilar fractions
Subtracting dissimilar fractionsNicko Salazar
油
The document shows steps to simplify fractions by finding a common denominator and multiplying the numerators. It provides examples such as simplifying 8/34 by finding the lowest common denominator of 34 and 8, which is 8. Then it multiplies the numerator 4 by 3 to get the simplified fraction of 6/8. It demonstrates this process on additional examples of simplifying fractions.[ETHCon Korea 2019] Bae kyungil 覦郁化
[ETHCon Korea 2019] Bae kyungil 覦郁化ethconkr
油
Secure multi-party computation allows multiple parties to jointly compute a function over their private inputs while preserving privacy. This is achieved through techniques like secret sharing, garbled circuits, and secure multi-party protocols. Recent improvements have increased performance, enabling practical applications in domains like genome analytics, smart cities, and blockchain where privacy-sensitive data from different entities must be analyzed without being shared in the clear.Solving Trinomial Equations
Solving Trinomial Equationsjames.northrup
油
1. The document shows the steps to solve a quadratic equation using algebra tiles.
2. It represents the equation x2 + 5x + 6 = 0 with algebra tiles, grouping like terms to write it as (x + 2)(x + 3) = 0.
3. It then solves for x by finding the two numbers whose product is zero, determining x = -2 or -3.General-Trinomials for public schoolpptx
General-Trinomials for public schoolpptxAxelJonCorpuz2
油
The document outlines a method for factoring trinomials of the form ax族 + bx + c, specifically when a = 1. It provides step-by-step instructions for determining the factors through the FOIL method and includes various examples with practice problems and solutions. The document also briefly mentions factoring techniques for polynomials with four or more terms.factoring and the other ones polynomials2.ppt
factoring and the other ones polynomials2.pptScience18
油
The document discusses various methods for factoring polynomials:
1) Factoring out the greatest common factor (GCF) of each term.
2) Using the difference of squares formula a2 - b2 = (a + b)(a - b).
3) Grouping terms to produce common binomial factors.
4) Reversing the FOIL process to factor trinomials of the form x2 + bx + c.
5) Factoring polynomials completely by factoring out the GCF and then factoring the remaining terms.Polynomial math
Polynomial mathNeil MacIntosh
油
1) The document discusses various methods for manipulating and solving algebraic expressions, including adding, subtracting, and factoring polynomials.
2) Factoring techniques include grouping like terms, using the difference of squares formula, and recognizing perfect square trinomials.
3) The quadratic formula is introduced as a way to solve quadratic equations of the form ax2 + bx + c = 0.Factoring and Box Method
Factoring and Box Methodswartzje
油
This document discusses various techniques for factoring polynomials, including:
1. Factoring using the greatest common factor (GCF).
2. Factoring polynomials with 4 or more terms by grouping.
3. Factoring trinomials using factors that add up to the coefficient of the middle term.
4. Using the "box method" to factor trinomials where the coefficient of the x^2 term is not 1.
5. Factoring the difference of two squares using the formula a^2 - b^2 = (a + b)(a - b).More Related Content
What's hot (18)
BBMP1103 - Sept 2011 exam workshop - part 7
BBMP1103 - Sept 2011 exam workshop - part 7Richard Ng
油
This document summarizes an exam preparation workshop on the application of partial differentiation presented by Dr. Richard Ng. It provides the answers to two sample exam questions, finding the critical points and determining whether they are maxima or minima for multivariate functions. For the first question, the critical point is found to be (7/3, 8/3) which is a minimum. For the second question, the critical point is (-4, 2) which is also determined to be a minimum using the second derivative test.BBMP1103 - Sept 2011 exam workshop - Part 2
BBMP1103 - Sept 2011 exam workshop - Part 2Richard Ng
油
This document is a summary of key points from a mathematics exam preparation workshop on differentiation:
1) It provides the solutions to sample differentiation problems, finding the first and second derivatives of functions like f(x)=5x^3 and p(x)=5x^3-3x^2+7/x^2.
2) It also gives the solutions to differentiation questions that were part of past mathematics exams, finding derivatives like dy/dx of functions such as y=(x^3)(4x^2-2x).
3) The document aims to help students preparing for exams by providing worked examples of common differentiation questions and techniques for finding derivatives.Maximum and minimum
Maximum and minimumshirleyaporter
油
This document discusses using quadratic functions to find the minimum and maximum values without using much algebra. It shows that for the basic quadratic function y=x^2, the minimum value is found at x=0 and the minimum value is y=0. Adding a negative sign in front of x^2 inverts the graph, and the maximum value is found at x=0. Adding a constant inside the quadratic function slides the graph along the x-axis in the opposite direction of the constant.June 5, 2014
June 5, 2014khyps13
油
The document provides instruction on simplifying rational expressions and equations, including complex fractions. It reviews concepts like multiplication and division of rational expressions, addition and subtraction of rational expressions, finding the lowest common denominator, and working with complex fractions. Examples are provided to demonstrate these concepts and techniques for simplifying rational expressions and solving rational equations.Rational Inequality Apr 20 09
Rational Inequality Apr 20 09ingroy
油
The document discusses solving rational inequalities by:
1) Placing critical numbers on a number line
2) Solving the inequalities algebraically
3) Graphing the solutions on the number line between the critical numbers5 Polynomial Feb 18
5 Polynomial Feb 18mskarras
油
This document provides a summary of factoring techniques including:
1) Squaring binomials using the formula (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) Factoring the difference of squares using the formula (a2 - b2) = (a + b)(a - b).
3) Factoring trinomials that are the product of a sum and difference using the formulas a2 - b2 = (a + b)(a - b).
4) Cubing a binomial using the formula (a + b)3 = a3 + 3a2b5 Polynomial Feb 22
5 Polynomial Feb 22mskarras
油
This document provides a summary of factoring techniques including:
1) Squaring binomials using the formula (a + b)2 = a2 + 2ab + b2 and (a - b)2 = a2 - 2ab + b2.
2) Factoring the difference of squares using the formula (a2 - b2) = (a + b)(a - b).
3) Factoring trinomials that are the product of a sum and difference using the formulas a2 - b2 = (a + b)(a - b).
4) Expanding cubes using the formula (x + a)3 = x3 + 3x2a +Divisi坦n de un polinomio entre un binomio
Divisi坦n de un polinomio entre un binomioprofesorluis
油
The document is a video cast that demonstrates dividing a polynomial by a binomial. It shows the step-by-step operations to divide the polynomial 5x^3 - 2x^2 + 3x + 1 by the binomial x + 1. The division results in the quotient of 5x^2 - 7x + 10 and the remainder of 0x - 9. The video cast provides credit to the source of an image and details about the software and music used.Day 11 factoring trinomials
Day 11 factoring trinomialsErik Tjersland
油
This document provides instructions for factoring trinomials using the method of finding two numbers whose product is the constant term and whose sum is the coefficient of the linear term. It includes examples of factoring various trinomials of the form x^2 + bx + c into the product of binomial factors (x + p)(x + q). The document aims to teach readers how to factor trinomials by finding the two numbers p and q that satisfy the given conditions.Day 3 subtracting polynomials
Day 3 subtracting polynomialsErik Tjersland
油
This document provides examples of subtracting polynomials. It begins with examples of subtracting terms like x+7 and 3x+9. It then shows how to subtract polynomials by removing corresponding terms and using the opposite sign. For example, (3x^2 + x + 2) - (2x^2 - x + 3) is solved by removing the 2x^2 terms and changing the sign of the remaining terms to get x^2 + x - 1. It provides several more examples and problems for students to solve, including finding the area of a shaded region between a rectangle and square using polynomial subtraction.Topic 3 factoring perfect square & difference of square
Topic 3 factoring perfect square & difference of squareAnnie cox
油
This document provides instruction on factoring perfect square trinomials and difference of squares expressions. It includes links to video explanations of factoring perfect square trinomials. It provides examples of factoring a perfect square trinomial and difference of squares expressions, including step-by-step worked examples. Students are instructed to practice these skills using online factoring activities and games in order to correctly factor 4 out of 5 problems.Factoring trinomials
Factoring trinomialsguest7c2aac
油
This document provides instructions for factoring a trinomial. It gives the example of factoring x^2 + 7x - 18. The steps shown are writing out the trinomial, finding the greatest common factor of the first and last terms, then using that to write the trinomial as the product of two binomials, (x - 2)(x + 9), which provides the factored form of the original trinomial.C8 8.6
C8 8.6BGEsp1
油
This document contains 6 math word problems asking the reader to divide various polynomial expressions. Each problem is followed by the word "Solution" indicating the answer or worked out steps are to follow. The problems involve dividing expressions such as x^2 - 5x + 6 by x - 3, ax^2 - ay^2 by ax + ay, and (a^2 + 2ab + b^2) - (a^2 + 2ac + c^2) by 2a + b + c.Adding dissimilar fractions
Adding dissimilar fractionsNicko Salazar
油
The document shows steps to solve several fraction addition problems by finding a common denominator. It first shows 3814+ = n, finds the lowest common denominator of 8, and sets up the equivalent fractions with that denominator to solve. It then works through several more examples using the same process of finding the common denominator and setting up equivalent fractions to solve.Subtracting dissimilar fractions
Subtracting dissimilar fractionsNicko Salazar
油
The document shows steps to simplify fractions by finding a common denominator and multiplying the numerators. It provides examples such as simplifying 8/34 by finding the lowest common denominator of 34 and 8, which is 8. Then it multiplies the numerator 4 by 3 to get the simplified fraction of 6/8. It demonstrates this process on additional examples of simplifying fractions.[ETHCon Korea 2019] Bae kyungil 覦郁化
[ETHCon Korea 2019] Bae kyungil 覦郁化ethconkr
油
Secure multi-party computation allows multiple parties to jointly compute a function over their private inputs while preserving privacy. This is achieved through techniques like secret sharing, garbled circuits, and secure multi-party protocols. Recent improvements have increased performance, enabling practical applications in domains like genome analytics, smart cities, and blockchain where privacy-sensitive data from different entities must be analyzed without being shared in the clear.Solving Trinomial Equations
Solving Trinomial Equationsjames.northrup
油
1. The document shows the steps to solve a quadratic equation using algebra tiles.
2. It represents the equation x2 + 5x + 6 = 0 with algebra tiles, grouping like terms to write it as (x + 2)(x + 3) = 0.
3. It then solves for x by finding the two numbers whose product is zero, determining x = -2 or -3.Similar to 5 6 slideand_divide_11_19_12 (20)
General-Trinomials for public schoolpptx
General-Trinomials for public schoolpptxAxelJonCorpuz2
油
The document outlines a method for factoring trinomials of the form ax族 + bx + c, specifically when a = 1. It provides step-by-step instructions for determining the factors through the FOIL method and includes various examples with practice problems and solutions. The document also briefly mentions factoring techniques for polynomials with four or more terms.factoring and the other ones polynomials2.ppt
factoring and the other ones polynomials2.pptScience18
油
The document discusses various methods for factoring polynomials:
1) Factoring out the greatest common factor (GCF) of each term.
2) Using the difference of squares formula a2 - b2 = (a + b)(a - b).
3) Grouping terms to produce common binomial factors.
4) Reversing the FOIL process to factor trinomials of the form x2 + bx + c.
5) Factoring polynomials completely by factoring out the GCF and then factoring the remaining terms.Polynomial math
Polynomial mathNeil MacIntosh
油
1) The document discusses various methods for manipulating and solving algebraic expressions, including adding, subtracting, and factoring polynomials.
2) Factoring techniques include grouping like terms, using the difference of squares formula, and recognizing perfect square trinomials.
3) The quadratic formula is introduced as a way to solve quadratic equations of the form ax2 + bx + c = 0.Factoring and Box Method
Factoring and Box Methodswartzje
油
This document discusses various techniques for factoring polynomials, including:
1. Factoring using the greatest common factor (GCF).
2. Factoring polynomials with 4 or more terms by grouping.
3. Factoring trinomials using factors that add up to the coefficient of the middle term.
4. Using the "box method" to factor trinomials where the coefficient of the x^2 term is not 1.
5. Factoring the difference of two squares using the formula a^2 - b^2 = (a + b)(a - b).1.3 Factoring Polynomial and Quadratic Expressions
1.3 Factoring Polynomial and Quadratic Expressionssmiller5
油
Review factoring polynomial and quadratic expressions.1.5 Factoring Polynomials
1.5 Factoring Polynomialssmiller5
油
The document provides a comprehensive overview of factoring polynomials, including methods such as factoring out the greatest common factor, factoring by grouping, and factoring trinomials using various techniques. It explains specific patterns for perfect square trinomials and binomials, and offers examples to illustrate each method. Additionally, it indicates the importance of checking factors by multiplying to ensure accuracy in the factoring process.Polynomials Grade 10
Polynomials Grade 10ingroy
油
This document provides instructions on how to multiply, divide, and factor polynomials. It discusses:
1) Multiplying polynomials by distributing terms and using FOIL for binomials.
2) Dividing polynomials using long division.
3) Factoring polynomials using grouping, finding two numbers whose product is the constant and sum is the coefficient, and recognizing difference of squares.0.3 Factoring Polynomials
0.3 Factoring Polynomialssmiller5
油
This document provides an overview of various techniques for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF);
2) Factoring by grouping terms with a common factor;
3) Factoring perfect square trinomials where the first and last terms are perfect squares;
4) Factoring trinomials using techniques like the reverse box method or grouping.0.4 Factoring Polynomials
0.4 Factoring Polynomialssmiller5
油
This document provides an overview of various techniques for factoring polynomials, including:
1) Factoring out the greatest common factor (GCF);
2) Factoring by grouping terms;
3) Factoring trinomials using methods like the X-method or reverse box method;
4) Factoring perfect square trinomials by taking the square root of the first and last terms;
5) Factoring binomials using patterns like difference of squares or sum/difference of cubes; and
6) Factoring by substitution, where an expression is substituted for an easier to factor expression.
Examples are provided to demonstrate each technique. The document concludes by assigning related classwork and homework.Factoring
Factoringholmsted
油
The document discusses various factoring techniques, including:
- Factoring by greatest common factor (GCF)
- Factoring trinomials of the form ax^2 + bx + c by finding two numbers that multiply to c and add to b
- Factoring the difference of two squares and perfect square trinomials
- Using the "box method" to factor trinomials by placing factors of the first and last terms in the boxes
- Factoring by grouping polynomials with four terms into two groups of two terms each.Factoring 15.3 and 15.4 Grouping and Trial and Error
Factoring 15.3 and 15.4 Grouping and Trial and Errorswartzje
油
This document discusses various methods for factoring trinomials of the form Ax^2 + Bx + C. It begins by outlining three main methods: trial and error, factoring by grouping, and the box method. It then provides examples of using the factoring by grouping method, demonstrating how to find two numbers whose product is AC and sum is B. The document also covers special cases like factoring the difference of squares using the form A^2 - B^2 = (A-B)(A+B), and factoring perfect square trinomials using the form A^2 + 2AB + B^2 = (A+B)^2. In all, it thoroughly explains the step-byVargas chris
Vargas chrisLeslie Vargas
油
This document discusses different methods for factoring polynomials, including factoring by grouping and factoring trinomials. It provides examples and step-by-step solutions for factoring polynomials with four or more terms using grouping, as well as for factoring trinomials of the form x^2 + bx + c. The key steps for factoring by grouping and for factoring trinomials are outlined.March 17, 2015
March 17, 2015khyps13
油
Today's class will include a warm-up, factoring polynomials using the greatest common factor (GCF) method and factoring by grouping, and Khan Academy assignments due tonight. Students should show all their work to receive credit for class work involving factoring polynomials using GCF and grouping methods.Remainder and factor theorem
Remainder and factor theoremSarah Sue Calbio
油
The remainder theorem states that when a polynomial f(x) is divided by a linear expression (x - a), the remainder is f(a).
Some key points:
- If x - a is a factor of f(x), then f(a) = 0 according to the factor theorem
- Examples show using the remainder theorem to find the remainder when an expression is divided
- The factor theorem states that x - a is a factor of f(x) if and only if f(a) = 0
- Examples demonstrate determining if an expression is a factor and finding all factors1.3 Factoring Quadratics (Presentation).pdf
1.3 Factoring Quadratics (Presentation).pdfsmiller5
油
Review factoring polynomial and quadratic expressions.Section 61.pptlllllllllllllllllllllllllllllllllllllll
Section 61.pptlllllllllllllllllllllllllllllllllllllllJezVa
油
The document provides an overview of finding the greatest common factor (GCF) and factoring by grouping for polynomials. It explains methods for determining the GCF, including listing factors and prime factorization, and offers steps for factoring expressions using the GCF. Additionally, it includes examples to illustrate techniques for grouping terms and factoring polynomials effectively.Factoring-and-Finding-Roots-of-Polynomials.pptx
Factoring-and-Finding-Roots-of-Polynomials.pptxRegine Jolbitado
油
The document discusses factoring and finding roots of polynomial expressions, including the definitions of polynomials, factors, roots, and zeros. It explains various factoring methods, such as finding the greatest common factor (GCF), factoring differences of squares, and employing the quadratic formula. The document also provides examples and exercises to illustrate these concepts, ultimately highlighting how the roots and zeros of polynomials relate to their graphical representations.1.5 Quadratic Equations (Review)
1.5 Quadratic Equations (Review)smiller5
油
This document provides instruction on factoring quadratic equations. It begins by reviewing factoring polynomials and trinomials. It then discusses factoring binomials using difference of squares, sum/difference of cubes, and other patterns. Finally, it explains that a quadratic equation can be solved by factoring if it can be written as a product of two linear factors. An example demonstrates factoring a quadratic equation by finding the two values that make each factor equal to zero.Ad
5 6 slideand_divide_11_19_12
- 1. 1. Check your grade 2. Be ready to take notes when the bell rings. Objective: SWBAT factor trinomials of the form using the slide and divide method 2 ax bx c+ +
- 2. Example #1 Factor 2 2 11 15x x+ + 1. GCFs? 2. 際際滷 3. Factor 4.Divide & simplify 5. Push back 6. Check 2 2 11 15x x+ + 1 1 1 No! 2 2 11 15x x+ + 2 11 30x x+ + 2 11 30x x+ + ( )( )x x ( 6)( 5)x x+ + 6+5=11 6*5=30 ( 6)( 5)x x+ + 2 2 5 ( 3)( ) 2 x x+ + 5 ( 3)( ) 2 x x+ + ( 3)(2 5)x x+ + ( 3)(2 5)x x+ + 2 2 5 6 15x x x+ + + 2 2 11 15x x+ + Correct
- 3. Example #2 Factor 2 3 4x x 2 3 4x x No GCF 際際滷 2 12x x ( )( )x x Factor ( 3)( 4)x x+ Divide & simplify ( 3)( 4)x x+ 3 3 4 ( 1)( ) 3 x x+ Push back 4 ( 1)( ) 3 x x+ ( 1)(3 4)x x+ Check: ( 1)(3 4)x x+ 2 3 4 3 4x x x + 2 3 4x x
- 4. Example #3 Factor 1. GCFs? 2. 際際滷 3. Factor 4.Divide & simplify 5. Push back 6. Check 4 3 2 12 42 18x x x+ + 4 3 2 12 42 18x x x+ + Yes! 2 6x 2 6x 2 6x 6+1=7 6*1 = 6 2 2 6 (2 7 3)x x x+ + 2 2 6 (2 7 3)x x x+ + ( )2 2 6 7 6x x x+ + ( )2 2 6 7 6x x x+ + 2 6 (x x )( )x 2 6 ( 6)( 1)x x x+ + 2 6 ( 6)( 1)x x x+ + 2 2 2 1 6 ( 3)( ) 2 x x x+ + 2 1 6 ( 3)( ) 2 x x x+ + 2 6 ( 3)(2 1)x x x+ + 2 6 ( 3)(2 1)x x x+ + 2 2 6 (2 6 1 3)x x x x+ + + 2 2 6 (2 7 3)x x x+ + 4 3 2 12 42 18x x x+ +
- 5. Example #4 Factor 3 2 12 22 8x y x y xy + 3 2 12 22 8x y x y xy + 2xy 2xy 2xy GCF 2 2 (6 11 4)xy x x + 際際滷2 2 ( 11 24)xy x x + Factor2 ( 8)( 3)xy x x 6 6 2 ( 8)( 3)xy x x Divide and simplify 4 1 2 ( )( ) 3 2 xy x x 4 1 2 ( )( ) 3 2 xy x x Push back 2 (3 4)(2 1)xy x x Check: 2 (3 4)(2 1)xy x x 2 2 (6 3 8 4)xy x x x + 2 2 (6 11 4)xy x x + 3 2 12 22 8x y x y xy +
- 6. Write a 2-3 sentence summary at the bottom of your notes Exercises p. 328 #25-39 odds (GREEN ALGEBRA BOOK)
- 7. Write a 2-3 sentence summary at the bottom of your notes Exercises p. 328 #25-39 odds (GREEN ALGEBRA BOOK)