Question

How do you factor `20x^2 + 22x - 12`?

Answer 1

Factor f(x) = 20x^2 + 22x - 12

Ans: f(x) = 2(5x - 2)(2x + 3)

Explanation:

`f(x) = 2y = 2(10x^2 + 11x - 6)`
Factor `y = 10x^2 + 11x - 6 =` (10(x + p)(x + q)
Converted trinomial `y' = x^2 + 11x - 60 =` (x + p')(x + q').
P' and q' have opposite signs. Factor pairs of (-60) --> (-3, 20)(-4, 15). This sum is (15 - 4 = 11 = b). Then p' = -4 and q' = 15. Therefor,
`p = p = (p')/a = -4/10 = -2/5` and `q = 15/10 = 3/2`.
Factored form `y = 10(x - 2/5)(x + 3/2) = (5x - 2)(2x + 3).`
Finally:
`f(x) = 2(5x - 2)(2x + 3)`