1. 5-4 Factoring Polynomials Objectives: Students will be able to: 1)Factor polynomials 2)Simplify polynomial quotients by factoring

2. Factorin g  There are several different techniques used to factor polynomials.  The technique(s) used depend on the number of terms in the polynomial, and what those terms are.  The following is a brief review of the factoring methods you learned in Algebra I.

3. GCF  Greatest common factor: largest factor that all terms have in common  May be used for a polynomial of two or more terms.  Steps: 1) determine what the GCF of the terms is, & factor it out (divide each term by the GCF) 2) rewrite the expression using the distributive property

6. Grouping  factoring technique used when a polynomial contains four or more terms.  Steps: (based on a polynomial of four terms) 1) group terms with common factors (separate the polynomial expression into two separate expressions) 2) factor the GCF out of each expression 3) rewrite the expression using the distributive property (factor into a binomial multiplied by a binomial)

8. More Grouping Examples:

10. Try these.

11. Factoring Trinomials  The standard form for a trinomial is:  Goal: factor it into two binomials.  In order to factor, we need to “bust” our b term. Steps : 1) Multiply a X c 2) Look for factors of the product in step 1 that add to give you the ‘b’ term. 3) Rewrite the ‘b’ term using these factors. 4) Factor by grouping.

15.  There are instances when a polynomial will have a GCF that can be factored out first. Doing so will make factoring a trinomial much easier. Factor each polynomial

16. Now that you are factoring experts, try this one…

17. Additional Techniques  There are certain binomials that are factorable, but cannot be factored using any of the previous factoring techniques.  For these, we must apply the following patterns: When no factoring techniques or patterns apply, the polynomial is said to be PRIME.

20. Simplify each rational expression

21. Try this...