Question

How do you factor `16x^2 - 28x - 8`?

Answer 1

Factor `y = 16x^2 - 28x - 8`

Explanation:

`f(x) = 4y = 4(4x^2 - 7x - 2)`
Factor `y = 4x^2 - 7x - 2 =` 4(x + p)(x + q)
I use the new AC Method to factor trinomials (Socratic Search).
Converted trinomial `y' = x^2 - 7x - 8.`
Factor pairs of (-8) --> (-1, 8). This sum is 7 = -b. Then p' = 1 and q' = -8
Therefor `p = 1/4` and `q = -8/4 = - 2`
Factored form of `y = 4(x + 1/4)(x - 2) = (4x + 1)(x - 2).`
Finally:
`f(x) = 4(4x + 1)(x - 2)`