# How do you factor 16+ 22x - 3x ^ { 2}?

Jul 25, 2017

$- \left(3 x + 2\right) \left(x - 8\right)$

#### Explanation:

$f \left(x\right) = - y = - \left(3 {x}^{2} - 22 x - 16\right)$
Factor y by the new AC Method (Socratic Search)
$y = 3 {x}^{2} - 22 x - 16 =$ 3( x + p)(x + q)
Converted trinomial:
$y ' = {x}^{2} - 22 x - 48 =$ (x + p')(x + q')
Proceeding: Find p' and q', then, divide them by a = 3.
Find p' and q', knowing the sum (b = -22) and the product (ac = -48). They are: p' = 2 and q' = - 24.
Back to y --> $p = \frac{p '}{a} = \frac{2}{3}$, and $q = - \frac{24}{3} = - 8$
Factored form:
$y = 3 \left(x + \frac{2}{3}\right) \left(x - 8\right) = \left(3 x + 2\right) \left(x - 8\right)$
Finally,
$f \left(x\right) = - \left(3 x + 2\right) \left(x - 8\right)$