Question

How do you factor completely `6x^2-2x-20`?

Answer 1

2(3x + 5)(x - 2)

Explanation:

`f(x) = 2y = 2(3x^2 - x - 10).`
Factor the trinomial y, in parentheses, by the new AC method (Socratic Search).
`y = 3x^2 - x - 10 =` 3(x + p)(x + q)
Converted trinomial: `y' = x^2 - x - 30 =` (x + p')(x + q')
Find p' and q', knowing their sum (-1) and their product (-30).
They are: p' = 5 and q' = -6.
Back to y, --> `p = (p')/a = 5/3` and `q = (q')/a = -6/3 = -2`.
Factored form: `y = 3(x + 5/3)(x - 2) = (3x + 5)(x - 2)`
Finally,
`f(x) = 2(3x + 5)(x - 2)`