1. 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 = 12, and 7 x 5 = 35
Thus, x2 + 12x + 35= (x + 5)(x + 7)

2. 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)

3. 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

4. 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)