Question

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

Answer 1

`- (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)`