Question

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

Answer 1

Factor`y = 4x^2 + 4x - 15`

Explanation:

`y = 4x^2 + 4x - 15 =` 4(x - p)(x - q)
I use the new AC Method to factor trinomials.
Converted trinomial `y' = x^2 + 4x - 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 = (p')/a = -6/4 = -3/2` and `q = (q')/a = 10/4 = 5/2.`
Factored form: `y = 4(x - 3/2)(x - 5/2) = (2x - 3)(2x + 5)`

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