1. Factoring Quadratic Trinomials To Factor Trinomials in the Form x² + bx + c. OBJECTIVE C can be positive or negative

2. Method for Factoring x² + bx + c The first terms will both be x. Write all the factors of the last term Use addition to find the pair of factors that equal the middle term

3. Factor completely. x² + 6x + 8 (x )(x ) Write all the factors of the last term 1 · 8 2 · 4 -1 · -8 -2 · -4 Since the last term is positive, the signs will be the same Since the middle term is positive, the signs will be positive. 1 · 8 2 · 4 1 + 8 = 9 2 + 4 = 6 + 2 + 4

4. Factor Completely x² - 6x + 8 (x )(x ) 1 · 8 2 · 4 -1 · -8 -2 · -4 Since the last term is positive the signs will be the same, and the signs will be the same as the middle term -1 · -8 -2 · -4 -1 + (-8) = -9 -2 + (-4) = -6 - 2 - 4

5. Factor Completely x² + 14x + 40 1 · 40 2 · 20 4 · 10 5 · 8 4 + 10 = 14 (x + 4)(x + 10) x² - 10x + 16 -1 · -16 -2 · -8 -4 · -4 -2 + (-8) = -10 (x – 2)(x – 8)

6. Factor Completely x² + 2x - 8 -1 · 8 Since the last term is negative, make sure you list all factors of the last term 1 · -8 -2 · 42 · -4 -2 + 4 = 2 (x – 2)(x + 4)

7. Factor Completely x² - x - 20 -1 · 201 · -20 -2 · 102 · -10 -4 · 54 · -5 4 + (-5) = -1 ( x + 4)(x – 5) x² + 4x - 21 -1 · 212 · -21 -3 · 73 · -7 -3 + 7 = 4 (x – 3)(x + 7)