Special factor patterns
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The document provides examples and rules for factoring different types of expressions: 1) It shows how to factor expressions of the form a^2 - b^2 into (a+b)(a-b) and gives an example. 2) It explains how to factor square trinomials of the form x^2 + bx + c by finding two factors of c that sum to b. 3) It discusses factoring expressions involving squares and how exponents work.
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This document provides information on various mathematical concepts including:
1. A monomial is the product of a real number and one or more variables. A polynomial contains more than one variable, constants, and exponents.
2. When adding or subtracting polynomials, like terms are combined. When multiplying polynomials, each term in one polynomial is multiplied by each term in the other and the results are added.
3. Fractions can be added by finding a common denominator and adding the numerators. Fractions are multiplied by multiplying the numerators and multiplying the denominators.
4. Equations can be solved using techniques like reduction, substitution, and factoring polynomials.
5. Factoring is the process of writing anMultiplying Polynomials
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The document provides examples and explanations of adding, subtracting, multiplying, and expanding polynomials. It demonstrates multiplying polynomials using the FOIL (First, Outer, Inner, Last) method and provides examples of sum and difference of squares, square of a binomial, cube of a binomial, and multiplying three binomials. Common patterns that arise when multiplying polynomials are identified.Class 9
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This document contains 54 multiple choice questions related to polynomials and their properties. Some key questions asked about:
- Finding the degree of polynomials
- Identifying the number of real zeros of polynomials
- Factoring polynomials
- Evaluating polynomials for given values
- Identifying coefficients and constants in polynomial expressions
- Relating the zeros of a polynomial to its factors
The questions cover topics like polynomial definitions, operations, factorization, finding zeros, and other properties of polynomials.Paso 2 profundizar y contextualizar el conocimiento de la unidad 1 ff
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This document provides an overview of algebraic expressions and factorization techniques covered in Unit 1. It defines basic algebraic expressions, polynomials, monomials, binomials, trinomials and more. It then describes 10 cases of factorization, including common factors, difference of squares, sum/difference of cubes, and more. Examples are provided for each case to demonstrate the factorization processes.Expresiones algebraicas
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The document defines algebraic expressions and provides examples of basic operations - addition, subtraction, multiplication, and division - that can be performed on algebraic expressions. It also covers evaluating algebraic expressions for given variable values and important algebraic identities called "notable products", including differences and sums of squares and cubes. Examples are given for each type of operation and identity.factoring trinomials the ac method and making lists
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This document discusses factoring trinomials. It defines a trinomial as a three-term polynomial of the form ax2 + bx + c, where a, b, and c are numbers. There are two types of trinomials: those that are factorable, which can be written as the product of two binomials, and those that are prime or unfactorable. The document outlines the basic rules for factoring trinomials and provides an example of expanding a binomial expression into a trinomial.Algebra unit 8.7
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This document provides examples and explanations for factoring special cases of polynomials, including perfect square trinomials and the difference of two squares. It includes examples of recognizing, factoring, and explaining if expressions are in one of these forms. One example problem finds the perimeter of a garden given its area as a factored expression and evaluates the perimeter for a given value of x.Algebra slideshow
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The document provides instructions for graphing and solving various types of quadratic equations. It defines standard form, vertex form, and intercept form of quadratics. It explains how to graph quadratics by finding the vertex and intercepts. Methods covered include factoring, taking square roots, completing the square, and using the quadratic formula. Examples are included to demonstrate each process.Expresiones algebraicas pdf
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This document discusses algebraic expressions, factorization, and radicals. It defines algebraic expressions and outlines rules for multiplying, dividing, and factoring algebraic expressions using notable products such as the difference of squares, sum and difference of cubes, and binomial squares. It also covers simplifying fractional algebraic expressions and operations involving fractions. Finally, it discusses factoring polynomials using the Ruffini method and summarizes rules for adding, subtracting, multiplying, and dividing radicals.Expresiones algebraicas y factorizacion
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Suma, resta y valor numérico de expresiones algebraicas.
multiplicación y división.
Producto notable de expresiones algebraicas.
Factorización por producto notable.Algebra 
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The document discusses algebra and its basic concepts. It begins by introducing algebra and defining it as the aspect of mathematics involving the use of numbers and letters. It then provides examples of solving algebraic puzzles using letters to represent unknown numbers. The document goes on to define key algebraic terms like constants, variables, coefficients and terms. It also outlines fundamental algebraic rules like commutativity, associativity and distributivity. It discusses how to collect like terms and factorize expressions. Finally, it covers topics like expanding and simplifying brackets, fractions and factorizing expressions.Produccion escrita expresiones algebraicas
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The document discusses various algebraic operations including:
1) Summing algebraic expressions by adding like terms.
2) Subtracting algebraic expressions by adding the opposite of like terms.
3) Multiplying algebraic expressions by multiplying each term in one factor by each term in the other factor.
4) Dividing algebraic expressions using long division.
Bonus math project
Bonus math projectKenton Hemsing
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This document provides an overview of different methods for solving quadratic equations, including factoring, graphing, using the quadratic formula, and more. It begins by defining the general and standard forms of quadratic equations. It then explains how to write equations in standard form and discusses concepts like the vertex, completing the square, determining zeroes/roots, and the discriminant. Finally, it reviews several methods that can be used to find roots of quadratic and higher-order polynomial equations, such as factoring, graphing, the quadratic formula, synthetic division, and the remainder/factor theorems.More from Cinnaminson Public Schools (20)
2015SupervisorResume
2015SupervisorResumeCinnaminson Public Schools
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Joshua W. Zagorski is a math teacher at Cinnaminson Township Public Schools in New Jersey. He has over 10 years of experience teaching mathematics at the middle and high school levels. He holds a Master's degree in Education from La Salle University and a Bachelor's degree in Sociology from Moravian College. Zagorski has received several honors for his teaching, including being named Teacher of the Year at Cinnaminson Middle School. He actively integrates technology into his classroom and has led initiatives to supplement math instruction.1.8 lab
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This document contains instructions for an experiment to measure the time it takes for a varying number of students to complete a task of standing, clapping, and sitting. Students will take turns performing the task until all have participated, and the time to complete each round will be recorded. The number of students is the independent variable and time is the dependent variable. Data for groups of 3 to 24 students will be plotted on a graph and the best fit line drawn to analyze the correlation between more students and longer completion times.Budget project
Budget projectCinnaminson Public Schools
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This document provides instructions for creating a realistic monthly budget. It explains that a budget accounts for income versus expenses, with the goal of expenses being less than income. Common expenses are listed like housing, utilities, transportation, food, and savings, which should be at least 5% of income. Students will be assigned an occupation with a set income and must choose housing, a car, and estimate other expenses to track in a monthly budget worksheet. If expenses exceed income or savings is less than 5%, spending habits must be adjusted.Scale drawing table
Scale drawing tableCinnaminson Public Schools
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This document provides instructions for creating a scale drawing of a piece of furniture. It notes that measurements should be provided in either boxes or inches, not both. As an example, a grey shelf that is 3 feet by 1 foot in real life would be drawn as either 3 boxes by 1 box or 0.75 inches by 0.25 inches on the scale drawing, since the scale factor is that 1 foot equals 1/4 inch or one box.Linear equation graphic
Linear equation graphicCinnaminson Public Schools
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A linear equation is represented by y = mx + b, where m is the coefficient that determines the steepness of the graph line, b is the y-intercept or the point at which the line crosses the y-axis, and x and y are coordinate pairs that each represent a single point on the line.
Scale drawing project
Scale drawing projectCinnaminson Public Schools
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This document provides instructions for a scale drawing project of a classroom floor plan. Students are asked to measure a classroom, determine an appropriate scale to fit the room on a piece of graph paper, and draw the outline of the room along with major furniture items using the scale. Students must include a scale bar, title, and colors to make the floor plan realistic. The project aims to provide floor plans of classrooms to facilitate school renovations.Scale drawing do nows
Scale drawing do nowsCinnaminson Public Schools
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Jenn had to create a scale drawing of her classroom for a school project. She measured her classroom and found it was 24 feet by 30 feet. To fit the drawing on graph paper, Jenn decided to use a scale of 1 foot equals 1/4 inch.Lifeline project grade sheet (2)
Lifeline project grade sheet (2)Cinnaminson Public Schools
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This grade sheet is for a lifeline project and assigns points to students for correctly graphing life events before and after their birth on a timeline, using accurate numerical representations and year intervals, as well as adding illustrations or labels for graphed events. It outlines the specific criteria students will be judged on, including correctly placing their birth at zero, graphing at least three pre-birth and six post-birth events, and creating a neat and creative final project.Lifelineproject
LifelineprojectCinnaminson Public Schools
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This document provides directions for creating a personal lifeline. Students must include their birth and at least 3 events that occurred before they were born, with each event listing the date as a fraction of years before or after the student's birth (assigned as 0). Events should have the month and year, the student's age at the event, and a brief description. Sample events include parents meeting, siblings being born, first teeth, words, bike riding, moves, vacations, or historical events. The lifeline may include one break and some photos.Polygons and quadrilaterals
Polygons and quadrilateralsCinnaminson Public Schools
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The document discusses polygons and quadrilaterals. It defines regular and irregular polygons, as well as convex and concave polygons. It then defines different types of quadrilaterals including trapezoids, rectangles, squares, rhombuses, and parallelograms. It provides three examples of finding the value of x and angle measures in different geometric shapes.L4 angles in polygons
L4 angles in polygonsCinnaminson Public Schools
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The document provides examples and explanations of geometry concepts including finding the perimeter of a regular octagon where one side is 12 cm, the triangle sum rule stating the interior angles of a triangle sum to 180 degrees, the definition of a diagonal as a line segment connecting two non-adjacent vertices of a polygon, and examples of finding the number of diagonals in nonagons and dodecagons.Congruent angles go
Congruent angles goCinnaminson Public Schools
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Vertical angles are angles that are opposite each other when two lines intersect. Corresponding angles are angles that are in the same relative position to the point of intersection but on opposite sides of the intersecting lines. Alternate exterior angles are nonadjacent angles outside of the intersecting lines formed by a transversal crossing two parallel lines. Alternate interior angles are nonadjacent angles inside of the intersecting lines formed by a transversal crossing two parallel lines.Lesson 3 line and angle relationships
Lesson 3 line and angle relationshipsCinnaminson Public Schools
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This document discusses different types of lines and their relationships. It defines parallel lines as two lines that lie in the same plane and do not intersect, intersecting lines as lines that cross paths at one point, and skew lines as lines that do not lie in the same plane and neither intersect nor are parallel. The document also notes that two points are needed to form a line and that two straight lines cannot intersect at more than one point.Angle relationships
Angle relationshipsCinnaminson Public Schools
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1) The document defines and provides examples of different types of angles including adjacent angles, complementary angles, supplementary angles, vertical angles, and angles formed when parallel lines are cut by a transversal.
2) It then provides practice problems involving calculating missing angles using properties such as angles summing to 90, 180 degrees, and the interior angles of triangles summing to 180 degrees.
3) The final problems involve identifying congruent, supplementary, and corresponding angles related to two parallel lines cut by a transversal.Angle relationships
Angle relationshipsCinnaminson Public Schools
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1) The document defines and provides examples of different types of angles including adjacent angles, complementary angles, supplementary angles, vertical angles, and angles formed when parallel lines are cut by a transversal.
2) It then provides practice problems involving calculating missing angles using properties such as angles summing to 90 or 180 degrees. Problems include solving for missing angles in triangles where the three interior angles sum to 180 degrees.
3) The last problems involve identifying properties of angles formed when two lines are parallel and cut by a transversal, such as naming congruent or supplementary angles.Building blocks of geometry
Building blocks of geometryCinnaminson Public Schools
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The document defines basic geometry terms including point, line, plane, ray, line segment, and angle. A point is represented by a dot at a location without size. A line extends in two opposite directions and is named by two points. A plane extends forever like a tabletop. A ray has one endpoint and extends forever in one direction, while a line segment connects two endpoints on a line.Sample questions 2013
Sample questions 2013Cinnaminson Public Schools
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The document contains 4 math word problems and their solutions:
1) Choosing 2 students from a group of 4 can be done in 6 combinations.
2) 15 - 3(2+1) = 15 - 3(3) = 15 - 9 = 6
3) A room measuring 8 feet 6 inches by 12 feet with 6-inch tiles needs 408 tiles.
4) A sequence with first terms 3, 5, 7, 9 has a rule of adding 2 to get the next term; a different sequence following the same rule of adding 2 would have first terms 5, 7, 9, 11, and the 100th term would be 198.7th ask prep jeopardy
7th ask prep jeopardyCinnaminson Public Schools
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The document contains a practice test for a 7th grade math assessment with 500 multiple choice questions covering topics like fractions, order of operations, geometry, probability, and more. Each question is numbered and includes 4 answer options with the correct answer indicated. The test reviews essential 7th grade math concepts and skills in a standardized multiple choice format.8th ask prep jeopardy
8th ask prep jeopardyCinnaminson Public Schools
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This document contains 100 math word problems and multiple choice questions from an 8th grade standardized test practice. It provides the question, possible answer choices, and the correct answer for each problem. The questions cover a range of math topics including arithmetic, algebra, geometry, statistics, probability, and measurement.Special factor patterns
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- 2. 1. Write as a Binomial: (9-w)(9+w) 2. Write each square as a trinomial: (6c-1) ² 3. Simplify: (y+4)(y+10)
- 3. a ²-b²  (a+b)(a-b) (First #)² - (Second #) ² = (sum of 2 squares) x (their difference)
- 4. Ex: 9a ² -4b ² =( 3a + 2b )(3a-2b) 3a is the square root of 9a ² and 2b is the square root of 4b ²
- 5. Ex: 36-25
- 6. 81-16 *** After you factor the number the first time, if there still is an a ²-b² in the subtraction binomial, you have to factor again until there are no squares left. ***
- 7. a ²+(-)2ab+b²  (a+(-)b)² If the middle number in the equation equals twice the square root of a times the square root of b, then you can factor it.
- 8. Ex: a ² +2a+1 = ( a+1 ) ² a and 1 are the square roots of the first and last numbers
- 9. Ex: u ² -6u+9
- 10. Ex: b ² +12b+4 This trinomial can’t be factored this way because the middle number does not equal twice the product of the first and last number.
- 11. Ex: 121c^4-264c ² +144 ^4 means to the fourth power****
- 12. x²+(-)bx+c  (x + factor of b that adds to c) (x +(-) factor of b that adds to c)
- 13. Ex: x ² +8x+15 = (x+ 3 ) (x+ 5 ) 5 and 3 add up to 8, and are a factor pair of 15.
- 14. Ex: x ² -10x+24
- 15. Ex: y ² +20yz+91z ²
- 16. Ex: x^4-15x ² y ² -16y^4
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