ch13powerpoint - Chapter 13 Factoring Polynomials Martin-Gay Developmental Mathematics 2 13.1 \u2013 The Greatest Common Factor 13.2 \u2013 Factoring

ch13powerpoint - Chapter 13 Factoring Polynomials...

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Chapter 13 Factoring Polynomials
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Martin-Gay, Developmental Mathematics 2 13.1 – The Greatest Common Factor 13.2 – Factoring Trinomials of the Form x 2 + bx + c 13.3 – Factoring Trinomials of the Form ax 2 + bx + c 13.4 – Factoring Trinomials of the Form x 2 + bx + c by Grouping 13.5 – Factoring Perfect Square Trinomials and Diff erence of Two Squares 13.6 – Solving Quadratic Equations by Factoring 13.7 – Quadratic Equations and Problem Solving Chapter Sections
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§ 13.1 The Greatest Common Factor
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Martin-Gay, Developmental Mathematics 4 Factors Factors (either numbers or polynomials) When an integer is written as a product of integers, each of the integers in the product is a factor of the original number. When a polynomial is written as a product of polynomials, each of the polynomials in the product is a factor of the original polynomial. Factoring – writing a polynomial as a product of polynomials.
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Martin-Gay, Developmental Mathematics 5 Greatest common factor – largest quantity that is a factor of all the integers or polynomials involved. Finding the GCF of a List of Integers or Terms 1) Prime factor the numbers. 2) Identify common prime factors. 3) Take the product of all common prime factors. If there are no common prime factors, GCF is 1. Greatest Common Factor
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Martin-Gay, Developmental Mathematics 6 Find the GCF of each list of numbers. 1) 12 and 8 12 = 2 · 2 · 3 8 = 2 · 2 · 2 So the GCF is 2 · 2 = 4. 2) 7 and 20 7 = 1 · 7 20 = 2 · 2 · 5 There are no common prime factors so the GCF is 1. Greatest Common Factor Example
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Martin-Gay, Developmental Mathematics 7 Find the GCF of each list of numbers. 1) 6, 8 and 46 6 = 2 · 3 8 = 2 · 2 · 2 46 = 2 · 23 So the GCF is 2. 2) 144, 256 and 300 144 = 2 · 2 · 2 · 3 · 3 256 = 2 · 2 · 2 · 2 · 2 · 2 · 2 · 2 300 = 2 · 2 · 3 · 5 · 5 So the GCF is 2 · 2 = 4. Greatest Common Factor Example
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Martin-Gay, Developmental Mathematics 8 1) x 3 and x 7 x 3 = x · x · x x 7 = x · x · x · x · x · x · x So the GCF is x · x · x = x 3 6 x 5 and 4 x 3 6 x 5 = 2 · 3 · x · x · x 4 x 3 = 2 · 2 · x · x · x So the GCF is 2 · x · x · x = 2 x 3 Find the GCF of each list of terms. Greatest Common Factor Example
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Martin-Gay, Developmental Mathematics 9 Find the GCF of the following list of terms. a 3 b 2 , a 2 b 5 and a 4 b 7 a 3 b 2 = a · a · a · b · b a 2 b 5 = a · a · b · b · b · b · b a 4 b 7 = a · a · a · a · b · b · b · b · b · b · b So the GCF is a · a · b · b = a 2 b 2 Notice that the GCF of terms containing variables will use the smallest exponent found amongst the individual terms for each variable. Greatest Common Factor Example
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Martin-Gay, Developmental Mathematics 10 The first step in factoring a polynomial is to find the GCF of all its terms. Then we write the polynomial as a product by factoring out the GCF from all the terms.
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