Section 6.1 Factoring Polynomials; Greatest Common Factor Factor By Grouping

Overview To factor a polynomial is to write it as the product of smaller polynomials, each of which itself cannot be factored further. A polynomial that cannot be factored is considered to be prime.

Factoring Strategies How a polynomial is factored is determined by the structure of the polynomials: Number of terms Degrees and coefficients of the terms In some cases, polynomials are factored using special patterns.

Greatest Common Factor Polynomial = GCF(Leftovers) The GCF is the largest monomial factor that will divide each term in the polynomial. Coefficients: use the GCF Common variables: choose the smallest exponent

Examples: Factor out the GCF 15r – 45 9z z 6p 3 – 3p 2 – 9p 4 14a 3 b 2 + 7a 2 b – 21a 5 b ab 4 2(5 – x) 3 – 3(5 – x) 2 -5a a 4 – 15a 5

Factor By Grouping Usually attempted when your polynomial has four terms term1 + term2 + term3 + term4 Factor out the GCF of the first two terms Factor out the GCF of the last two terms gcf1(leftovers) + gcf2(leftovers) (leftovers)(gcf1 + gcf2) You may have to rearrange the terms

Examples: Factor By Grouping m + 12n + 3mn 2a 3 + a 2 – 14a – 7 x 3 y 2 – 3 – 3y 2 + x 3

Very Important!!!!! Always look for a GCF before you attempt any other factoring strategy.