# How do you factor 8x^2 - 49x + 45?

May 10, 2016

(8x - 9)(x - 5)

#### Explanation:

Use the new AC Method to factor trinomials (Google, Yahoo Search).
$y = 8 {x}^{2} - 49 x + 45 =$8(x + p)(x + q)
Converted trinomial: $y ' = {x}^{2} - 49 x + 360 =$ (x + p')(x + q').
p' and q' have same sign because ac > 0.
Compose factor pairs of (ac = 360) --> ... (8, 45)(9, 40). This sum is
9 + 40 = 49 = -b. Then, the opposite pairs (-9, - 40) gives p' = -9 and q' = -40.
Back to original trinomial y, we get: $p = \frac{p '}{a} = - \frac{9}{8}$ and $q = \frac{q '}{a} = - \frac{40}{8} = - 5.$
Factored form $y = 8 \left(x - \frac{9}{8}\right) \left(x - 5\right) = \left(8 x - 9\right) \left(x - 5\right)$