Polynomials and linear factors
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The document discusses polynomials and their linear factors. It provides examples of polynomial functions with positive integer exponents like Ax^n+bx^n-1+cx^n-2. It also gives examples of specific polynomial functions like F(x)=1/2x^2+2x-3. The document notes that polynomials must have coefficients in descending order and defines what is not a polynomial, like functions with non-positive exponents. It also discusses finding the zeros of polynomials and defines vocabulary terms like degree and standard versus factored form.
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The document provides an overview of key concepts in algebra, including:
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3) Monomials, binomials, and polynomials are the main types of algebraic expressions. Operations like addition, multiplication, and factorization can be performed on these expressions.
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This document provides information about polynomials, including their standard form, degree, leading term, and the factor theorem. The degree of a polynomial is the highest exponent among its terms, and the leading term is the term with the highest degree and its coefficient. Examples demonstrate howMarch 6, 2014
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Light can travel 186,000 miles in one minute. In scientific notation, this is 1.86x105 miles.
The document discusses multiplying polynomials and binomials. It introduces the box method and the F.O.I.L (First, Outer, Inner, Last) method for multiplying binomials. F.O.I.L involves distributing the first term of one binomial with each term of the other binomial. The sign of the middle and last terms depends on whether the signs of the last terms of each binomial are the same or different.Polynomials
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Polynomials are mathematical expressions constructed from variables and constants using addition, subtraction, multiplication, and exponents of whole numbers. They appear in many areas of mathematics and science. Polynomials can be used to form equations that model problems in various domains. They also define polynomial functions that are used in fields like physics, chemistry, economics, and social sciences. Polynomials are classified based on their degree, with linear polynomials having degree 1 and quadratic polynomials degree 2. The maximum number of zeroes a polynomial can have is equal to its degree.Lesson 5.2 honors 2
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This document discusses how to solve quadratic equations by graphing. It defines the terms of a quadratic equation as the quadratic term, linear term, and constant term. Examples are given of identifying these terms in quadratic functions. The document also discusses that quadratic equations can have 0, 1, or 2 real solutions, which are found by determining where the graph crosses the x-axis. Methods for solving quadratic equations graphically include identifying the x-intercepts of the parabolic graph as well as using a table of x-values to plot the graph.Poly digi
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This document is a math project submitted by Aman Yadav of class 9A on polynomials. It covers topics like the definition of polynomials, exponents and terms, degree of polynomials in one and two variables, the remainder theorem, factor theorem, and algebraic identities. It provides examples and questions to explain these concepts. Key points are defined like a polynomial being the sum of monomials, and the degree being the highest power of a variable in a polynomial.Polynomials and linear factors
- 1. Polynomials and Linear FactorsBy: Daniel Yeiser
- 2. Example of a polynomial functionAx^n+bx^n-1+cx^n-2……………………if a,b, andc are real numbers n is a positive integer.
- 3. More examplesF(x)=1/2x^2+2x-3F(x)=6x^4-3x^2+2x-5F(x)=X^7-2F(x)=X^12The coefficients of the terms have to be put into a descending order.
- 4. Not PolynomialsF(x)=X^-2+5F(x)=2x^1/2+3x-4These are not polynomials because the exponents are not positive whole numbers
- 5. Zeros of polynomialsy=x-4. the zero of this one is 4Y=x+5. the zero of this one is -5Y=x^4-14x^2+30x this problem has 3 distinct zerosY=x^4-2x^3. this problem has exactly two zeros
- 6. Vocab. TermsDegree- highest power of x in standard formStandard form- everything in the problem is multiplied togetherFactored form looks like- f(x)=(x-r1) (x-r2)(x-r3)……….