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

Aug 6, 2015

#### Answer:

Factor$y = 4 {x}^{2} + 4 x - 15$

#### Explanation:

$y = 4 {x}^{2} + 4 x - 15 =$ 4(x - p)(x - q)
I use the new AC Method to factor trinomials.
Converted trinomial $y ' = {x}^{2} + 4 x - 60 =$ (x - p')(x - q')
Factor pairs of (-60) --> ...(-4, 15)(-5, 12)(-6, 10). This sum is 4 = b. Then p' = -6 and q' = 10.
Therefor, $p = \frac{p '}{a} = - \frac{6}{4} = - \frac{3}{2}$ and $q = \frac{q '}{a} = \frac{10}{4} = \frac{5}{2.}$
Factored form: $y = 4 \left(x - \frac{3}{2}\right) \left(x - \frac{5}{2}\right) = \left(2 x - 3\right) \left(2 x + 5\right)$

NOTE. This new AC Method can avoid the lengthy factoring by grouping