1. Introduction to Factoring Polynomials Section 10.4

2. Finding the Greatest Common Factor The first step in factoring a polynomial is to see whether the terms of the polynomial have a common factor. factoring out If there is a common factor, we can write the polynomial as a product by factoring out the common factor. We will usually factor out the greatest common factor (GCF). 2 Martin-Gay, Prealgebra, 5ed

3. Finding the Greatest Common Factor... greatest common factor (GCF) of a list of terms The greatest common factor (GCF) of a list of terms is the product of the GCF of the numerical coefficients and the GCF of the variable factors. Consider the terms, and. Common factors denoted by GCF 3

4. Helpful Hint Notice below that the GCF of a list of terms contains the smallest exponent on each common variable. The GCF of,, and is Smallest exponent on x. Smallest exponent on y. 4 Martin-Gay, Prealgebra, 5ed

5. Factoring Out the Greatest Common Factor Do the terms have a greatest common factor other than 1? To factor a polynomial: If so, factor out the greatest common factor from each term by writing each term as a product of the greatest common factor and the term’s remaining factors. Use the distributive property to write the factored form of the polynomial. 5

6. Factoring Out the Greatest Common Factor The GCF of 5x + 10 is 5. Consider, 5x + 10 Factor 5 from each term and write each term as a product of 5 and the remaining terms, Using the distributive property, write 5x + 10 factored form of polynomial Factoring can be checked by multiplying. Factoring can be checked by multiplying. 6

7. Helpful Hint A factored form of 5x + 10 is not terms polynomial Although the terms have been factored (written as a product), the polynomial 5x + 10 has not been factored. A factored form of product 5x + 10 is the product 5(x + 2). 5(x + 2) factored terms factored polynomial 7

8. Examples of Factored Polynomials Don’t forget the 1. Don’t forget the -1. Notice the changes in signs when factoring -2a In this example, factor out -2a rather than 2a In this example, factor out -2a rather than 2a 8