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

1 Answer
Apr 4, 2017

Answer:

(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)#