1. Purpose: To factor polynomials completely. Homework: P. 228 1-21 odd

2. Guidelines for Factoring 1. Look to factor the GCF first. If there is, look to further factor down. 2. If there is not a GCF, look for the differences of squares. 3. Look for the perfect square trinomial. 4. If the trinomial is not a square, use binomial factor pairs. 5. If the polynomial has more than 4 terms, find a way to group them.

3. Guidelines for Factoring 6. Make sure the binomial or trinomial is PRIME. 7. Check your work by multiplying the factors.

4. Examples 9ay² - 4a They both share an a. Pull it out first. a(9y² - 4) Always further factor. Differences of Squares. a(3y – 2)(3y + 2) -2x 4 – 12x 3 – 18x 2 They all share a -2x² -2x²(x² + 6x + 9) Always try to further factor. A Perfect Square -2x²(x + 3)(x + 3) = -2x²(x + 3)²

5. Examples 6n³ - 21n² - 45n They all share a 3n. 3n(2n² - 7n – 15) Always further factor. Binomial Pairs. 3n(2n ?)(n ?) You need a + and - 3n(2n + 3)(n – 5) x³y – xy + 5x²y – 5y Try Grouping. xy(x² - 1) + 5y(x² - 1) (xy + 5y)(x² - 1) You always want to further factor. y(x + 5)(x + 1)(x – 1)