Factoring By Grouping

1. Factoring By Grouping Students will be able to factor polynomials by grouping.

2. Steps in Factoring Polynomials • The first step in factoring a polynomial is to look for a common monomial factor. • If you find a GCF, extract it, as we did in the last section. • The next step is to look for a binomial factor, and extract it. • How do you find a binomial factor? Polynomials

3. Finding a binomial factor Follow these steps to find a binomial factor: • Group the terms in the polynomial into pairs with acommon factor. • Extract theGCFfrom each pair of terms. • If the binomials remaining for each pair are identical, that is thebinomial factor. • The monomials that have been extracted create a second polynomial. Polynomials

4. Example 1 Find the factors for 2a2+ 4ab + 3a + 6b • Group: • Find GCF for each group. The GCF for (2a2+ 4ab) is The GCF for (3a + 6b) is • Extract GCF from each pair. 2a(a + 2b) +3(a + 2b) • Extract binomial factor (2a2+ 4ab) + (3a + 6b) 2a 3 (a + 2b)(2a + 3) Polynomials

5. Example 2 Find the factors for 4x3+ 4x2y2– xy –y3 • Group: • Find GCF for each group. The GCF for (4x3+ 4x2y2) is The GCF for (xy +y3) is • Extract GCF from each pair. 4x2(x + y2) –y(x + y2) • Extract binomial factor (4x3+ 4x2y2) – (xy + y3) 4x2 y (x + y2)(4x2– y) Polynomials

6. Example 3 Find the factors for 2x3– 2x2y – 3xy2+ 3y3+ xz2– yz2 (2x3– 2x2y) – (3xy2– 3y3) + (xz2– yz2) 2x2(x– y)–3y2(x– y)+z2(x– y) (x – y) (2x2– 3y2+ z2) Polynomials