How do you factor 16+ 22x - 3x ^ { 2}?

1 Answer
Nghi N
Jul 25, 2017

- (3x + 2)(x - 8)

Explanation:

f(x) = - y = -(3x^2 - 22x - 16)
Factor y by the new AC Method (Socratic Search)
y = 3x^2 - 22x - 16 = 3( x + p)(x + q)
Converted trinomial:
y' = x^2 - 22x - 48 = (x + p')(x + q')
Proceeding: Find p' and q', then, divide them by a = 3.
Find p' and q', knowing the sum (b = -22) and the product (ac = -48). They are: p' = 2 and q' = - 24.
Back to y --> p = (p')/a = 2/3, and q = - 24/3 = - 8
Factored form:
y = 3(x + 2/3)(x - 8) = (3x + 2)(x - 8)
Finally,
f(x) = - (3x + 2)(x - 8)

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