1. Factoring Trinomials Chapter 10.4 Part 2

2. Review: Factoring Quadratic Trinomials Find the factors of the last term. Which of those factors combine to be the middle coefficient? Write as a product of binomials. x 2 – 10x + 16 = (x – 2)(x – 8) Factors of +16Sum of Factors (-1)(-16)-1 + (-16) = -17 (-2)(-8)-2 + (-8) = -10 (-4)(-4)-4 + (-4) = -8 Two numbers multiply to be positive, but add to a negative: Both are negative.

3. Factoring More Complicated Quadratic Trinomials 1. Try to factor out a GCF, if possible 2. Multiply the first and last terms. 3. Find the factors for this product. 4. Decide which factors add up to the middle. 5. Rewrite as a product of binomials. 3x 2 – 7x – 6 What if the first term has a coefficient other than 1? Step 1: 3x 2 – 7x – 6 has no GCF, other than 1.

4. Factoring More Complicated Quadratic Trinomials 2. Multiply the first and last terms. (3)(-6) = -18 3. Find the factors for this product. 4. Decide which factors add up to the middle. 3x 2 – 7x – 6 Factors of -18Sum of Factors (-1)(18)-1 + 18 = 17 (1)(-18)1 + (-18) = -17 (-2)(9)-2 + 9 = 7 (2)(-9)2 + (-9) = -7 (-3)(6)-3 + (6) = 3 (3)(-6)3 + (-6) = -3

5. Factoring More Complicated Quadratic Trinomials: 3x 2 – 7x – 6 5. Rewrite as product of binomials We need 4 factors: (__x +___) (__x +___) Factors of 2 & -9 (2)(1) (-3)(3) 3 The product of the FIRST numbers must be 3 (so 3 and 1.) The product of the LAST numbers must be -6 (2 and -3) The product of the INNER and OUTER must be 2 and -9. We should be able to FOIL our solution to get the original trinomial. 2-31

6. Homework: pg 484 (32-39 all, 43-48 all)