1. Chapter 8 Sections 5 & 6, Factoring Polynomials and Factors of Trinomials

2. Factoring Polynomials Overview  Reversing the multiplication of polynomials by monomials and/or binominals. Rewrite polynomials as the product of: Monomials Binomials Or polynomials with smaller exponents that the original Rules  Find Prime Factors of each term  Determine the prime factors common to all terms. The product of these factors is the Greatest Common Factor

3. Factoring Polynomials Rules  Divide the Polynomial by the ‘Greatest Common Factor’  Rewrite the polynomial as the product of the quotient in the above step and the Greatest Common Factor Walk through  Expression: 6a 2 + 12a – 18a 3 6a 2 = 2 * 3 * a * a 12a = 2 * 2 * 3 * a 18a 3 = 2 * 3 * 3 * a * a * a  6a is common to all factors, thus is the ‘Greatest Common Factor’

4. Factoring Polynomials

5. Factors of Trinomials Trinomials of the form x 2 + bx + c  Can be factored into (x + m)(x + n) n * m must equal c n + m must equal b  Trial trinomial x 2 + 13x + 42 See middle of page 172 for trials of n’s and m’s The two numbers must be 6 and 7 Thus: x 2 + 13x + 42 = (x + 7)(x + 6)

6. Factors of Trinomials Work Examples 8-24 thru 8-29

7. Factors of Trinomials