1College Algebra: Prerequisite Section 5: Factoring PolynomialsObjectives: Factor out the greatest common factor of a polynomial.Factor by grouping.Factor trinomials.Factor the difference of squaresFactor perfect square trinomials.Factor the sum or difference of two cubes.Use a general strategy for factoring polynomials.Factor algebraic expressions containing fractional and negative exponents.Factoringa polynomial expressed as the sum of monomials means finding an equivalent expression that is a product. We will be factoring over the set of integers, meaning that the coefficients in the factors are integers. Polynomials that cannot be factored using integer coefficients are called irreducible over the integers, or prime.The goal in factoring a polynomial is to use one or more factoring techniques until each of the polynomial’s factors, except possibly for a monomial factor, is prime or irreducible. In this situation, the polynomial is said to be factored completely.Common FactorsThe first step in factoring is to look for the greatest common factoror GCF. The GCF is an expression of the highest degree that divides each term of the polynomial. It is basically using the distributive property in reverse.ab + ac = a(b + c)Example 1: Factor the following:a. 10x3– 4x2b. 2x(x – 7) + 3(x – 7)

2Factoring by GroupingSome polynomials have only a greatest common factor of 1. However, if grouped properly, it may still be possible to factor. If your polynomial has 4 terms, try factoring