Question

How do you factor the trinomial `15x^3 - 22x^2 +8x`?

Answer 1

f(x) = x(3x - 2)(5x - 4)

Explanation:

`f(x) = x(y) = x(15x^2 - 22x + 8)`
Factor the trinomial y by the new AC Method (Socratic Search).
`y = (15x^2 - 22x + 8 =` 15(x + p)(x + q)
Converted trinomial `y' = x^2 - 22x + 120 =` (x + p')(x + q')
p'' and q' have same sign because ac > 0.
Factor pairs of (ac = 120) --> ...(8, 15) (10, 12). This sum is 22 = -b. The opposite sum (-10, -12) gives: p' = -10 and q' = -12.
Back to y, `p = p'/(a) = -10/15 = -2/3` and `q = (q')/a = -12/15 = -4/5`
Factored form: `f(x) = x(x - 2/3)(x - 4/5) = x(3x - 2)(5x - 4)`