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

1 Answer
Jul 25, 2017

Answer:

#- (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)#