MAT/117

University of Phoenix Material

Factoring

The goal of this week is to introduce the algebraic concept of factoring polynomials. Think of factoring as breaking a very complicated problem into its simple or basic parts.

What Is Factoring?

The basic idea of factoring is to rewrite an addition–subtraction problem as a multiplication problem.

Factors are the numbers that we multiply.

For example, 2 and 5 are the factors of 10 because 2 × 5 = 10. The addition of 6 and 4 can be written into the multiplication of 2 and 5:

6 + 4 = 2 × 5

In other words, we factored the addition 6 + 4 into the multiplication 2 × 5. The addition of 6 and 4 could have also been written into the multiplication of 1 x 10; however, the goal is always to find prime factors

(go to CME > Building Math Confidence > Phoenix Math – Topic 62).

The factors 1 and 10 are not prime factors of 10 (the answer of adding 6 and 4).

Factoring by GCF

The factoring process involves applying the distributive property that states