# How do you factor 2x^2-27x+36?

Jun 29, 2015

Factor: $y = 2 {x}^{2} - 27 x + 36$

#### Explanation:

$y = 2 {x}^{2} - 27 x + 36 =$ 2(x - p)(x - q)
I use the new AC Method to factor trinomials. (Google, Yahoo Search)
Converted $y ' = {x}^{2} - 27 x + 72$= (x - p')(x - q'). Roots have same sign (Rule of signs).
Factor pairs of ac = 72 -> (2, 36)(3, 24). This sum = 27 = -b.
p' = - 3 and q' = -24.
$p = - \frac{3}{2}$ and $q = - \frac{24}{2} = - 12$

Factored form: $y = 2 \left(x - \frac{3}{2}\right) \left(x - 12\right) = \left(2 x - 3\right) \left(x - 12\right)$