Question

How do you factor `8x^2 - 34x + 24 = -11`?

Answer 1

(4x - 7)(2x - 5)

Explanation:

Use the new AC Method to factor trinomials (Socratic Search).
`f(x) = 8x^2 - 34x + 35 = 8(x + p)(x + q)`
Converted trinomial `f'(x) = x^2 - 34x + 280 = (x + p')(x + q')`
Compose factor pairs of (ac = 280) --> ....(-10, -18)(-14, -20). This sum is (-35 = b). Then, p' = -14 and q' = -20.
Back to original f(x) --> `p = (p')/a = -14/8 = -7/4`, and
`q = (q')/a = -20/8 = - 5/2`.
Factored form:
`f(x) = 8(x - 7/4)(x - 5/2) = (4x - 7)(2x - 5)`