What is the factorization of the trinomial below - 2x^3-2x^2+12x

-2x^3 - 2x^2 + 12x

Because we can pull out a common factor, we'll do that first to simplify the expression.

-2x (x^2 + x - 6)

Now, let's see if we can split the middle term.

Display factors of - 6.

-6 * 1

-1 * 6

-3 * 2

3 * - 2 (these digits satisfy the requirements for splitting the middle term)

Split the middle term.

-2x (x^2 + 3x - 2x - 6)

Group terms in pairs of two.

-2x ((x^2 + 3x) - (2x - 6))

Factor each binomial.

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

Rearrange the terms.

-2x (x - 2) (x + 3) is the fully factored form of the provided trinomial.