4.3 Factoring Quadratics: x2+bx+c Factor x2 – 2x – 8: 2 numbers that multiply to -8 and add to -2 -4 and 2, since (-4) + 2 = -2, and (-4) x (2) = -8 Thus, x2 – 2x – 8 = (x + 2)(x – 4) Factor x2 + 12x + 35 2 numbers that multiply to +35 and add to +12 +7 and +5, since 7 + 5 = 12, and 7 x 5 = 35 Thus, x2 + 12x + 35= (x + 5)(x + 7)

Factoring Using Reasoning EX. Factor each expression, if possible. a) x2 – x – 72 Need 2 numbers that multiply to -72 and add to -1 -9 and 8, since (-9) x 8 = -72, and (-9) + 8 = -1 Thus, x2 – x – 72 = (x – 9)(x + 8) b) a2 – 13a + 36 Need 2 numbers that multiply to +36 and add to -13 -9 and -4, since (-9) x (-4) = 36, and (-9) + (-4) = -13 Thus, a2 – 13a + 36 = (a – 9)(a – 4)

Factoring Using Reasoning cont’d EX. Factor each expression, if possible. Cont’d. c) x2 + x + 6 Need 2 numbers that multiply to +6 and add to +1 Can’t be done because the only numbers whose product is +6 is 2 negative numbers or 2 positive numbers, who sum will not be 1

Putting Everything Together EX. Factor 3y3 – 21y2 – 24y 1st, notice that there is a GCF of 3y so divide it out 3y(y2 – 7y – 8) Now, we can factor the quadratic in brackets We need 2 numbers that multiply to -8 and add to -7 -8 and +1, since (-8) x 1 = -8, and (-8) + 1 = -7 (y2 – 7y – 8) = (y – 8)(y + 1) Thus, 3y3 – 21y2 – 24y = 3y(y – 8)(y + 1)