Factor the trinomial f (x) = 2x² + 5x - 12?

(x + 4) (2x - 3)

Step-by-step explanation:

Given

f (x) = 2x² + 5x - 12

Consider the factors of the product of the x² term and the constant term which sum to give the coefficient of the x - term.

product = 2 * - 12 = - 24 and sum = + 5

The factors are + 8 and - 3

Use these factors to split the x - term

2x² + 8x - 3x - 12 (factor the first/second and third/fourth terms)

2x (x + 4) - 3 (x + 4) ← factor out (x + 4) from each term

(x + 4) (2x - 3)

Thus

f (x) = 2x² + 5x - 12 = (x + 4) (2x - 3) ← in factored form