Factoring- Factoring Strategy

Objective: Identify and use the correct method to factor various polynomials.

With so many different tools used to factor, it is easy to get lost as to which tool to use when. Here we will attempt to organize all the different factoring types we have seen:

Greatest Common Factor

Factoring by Grouping

Factoring Trinomials

Factoring Special Products

A large part of deciding how to solve a problem is based on how many terms are in the problem. For all problem types we will always try to factor out the GCF first.

Example:

108x³y²39x²y²+3xy² GCF first, 3xy²

3xy² (36x²13x+1) Thee terms, ac method, multiply to 36, add to13

3xy² (36x²9x4x+1) 9 and4, split middle term

3xy² [9x (4x1) 1 (4x1)] Factor by grouping

3xy² (4x1) (9x1) Final Solution

Example:

5+625y³ GCF first, 5

5(1+125y³) Two terms, sum of cubes

5(1+5y) (15y +25y²) Final Solution

Factor completely showing all work:

20uv 60u³5xv +15xu²