# How do you factor 4x^2+17x-15?

Aug 5, 2015

Factor: y = 4x^2 + 17x - 15 (1)

Ans: (4x - 3)(x + 5)

#### Explanation:

y = 4(x - p)(x - q)
I use the new AC method to factor trinomials.
Converted trinomial: $y ' = {x}^{2} + 17 x - 60$= (x - p')(x - q')
p' and q' have opposite sign.
Factor pairs of -60 -->( -2, 30)(-3, 20). This sum is 17 = b.
Then p' = -3 and q' = 20
Therefor, $p = \frac{p '}{a} = - \frac{3}{4}$, and $q ' = \frac{20}{4} = 5$

$y = 4 \left(x - \frac{3}{4}\right) \left(x + 5\right) = \left(4 x - 3\right) \left(x + 5\right)$