# Chapter 4: Factoring Polynomials Factoring Polynomials Part 1 The Greatest Common Factor Greatest Common Factor 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. Martin-Gay, Developmental Mathematics 3

Greatest Common Factor Example Find the GCF of each list of numbers. 1) 12 and 8 2) 7 and 20 Martin-Gay, Developmental Mathematics

4 Greatest Common Factor Example Find the GCF of each list of numbers. 3) 6, 8 and 46 4) 144, 256 and 300 Martin-Gay, Developmental Mathematics

5 Greatest Common Factor Example Find the GCF of each list of terms. 1) x3 and x7 2)

6x5 and 4x3 Martin-Gay, Developmental Mathematics 6 Greatest Common Factor Example Find the GCF of the following list of terms. 3) a3b2, a2b5 and a4b7

Notice that the GCF of terms containing variables will use the smallest exponent found amongst the individual terms for each variable. Martin-Gay, Developmental Mathematics 7 Factoring Polynomials 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. The remaining factors in each term will form a polynomial. Martin-Gay, Developmental Mathematics 8

Factoring out the GCF Example Factor out the GCF in each of the following polynomials. 1) 6x3 9x2 + 12x = 2) 14x3y + 7x2y 7xy = Martin-Gay, Developmental Mathematics

9 Factoring out the GCF Example Factor out the GCF in each of the following polynomials. 3) 6(x + 2) y(x + 2) = 4) xy(y + 1) (y + 1) =

Martin-Gay, Developmental Mathematics 10 Part 1 Factoring Trinomials of the 2 Form x + bx + c

Factoring Trinomials Recall by multiplying two binomials F O I L

(x + 2)(x + 4) =. Martin-Gay, Developmental Mathematics 12 Factoring Polynomials Example Factor the polynomial x2 + 13x + 30.

Martin-Gay, Developmental Mathematics 13 Factoring Polynomials Example Factor the polynomial x2 11x + 24. Martin-Gay, Developmental Mathematics

14 Factoring Polynomials Example Factor the polynomial x2 2x 35. Martin-Gay, Developmental Mathematics 15

Prime Polynomials Example Factor the polynomial x2 6x + 10. Martin-Gay, Developmental Mathematics 16 Prime Polynomials Example

Factor the polynomial x2 10x + 25. Martin-Gay, Developmental Mathematics 17 Check Your Result! You should always check your factoring results by multiplying the factored polynomial to verify that it is equal to the original

polynomial. Many times you can detect computational errors or errors in the signs of your numbers by checking your results. Martin-Gay, Developmental Mathematics 18