# How do you factor 8x^2 - 34x + 24 = -11?

Apr 4, 2017

(4x - 7)(2x - 5)

#### Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
$f \left(x\right) = 8 {x}^{2} - 34 x + 35 = 8 \left(x + p\right) \left(x + q\right)$
Converted trinomial $f ' \left(x\right) = {x}^{2} - 34 x + 280 = \left(x + p '\right) \left(x + q '\right)$
Compose factor pairs of (ac = 280) --> ....(-10, -18)(-14, -20). This sum is (-35 = b). Then, p' = -14 and q' = -20.
Back to original f(x) --> $p = \frac{p '}{a} = - \frac{14}{8} = - \frac{7}{4}$, and
$q = \frac{q '}{a} = - \frac{20}{8} = - \frac{5}{2}$.
Factored form:
$f \left(x\right) = 8 \left(x - \frac{7}{4}\right) \left(x - \frac{5}{2}\right) = \left(4 x - 7\right) \left(2 x - 5\right)$