Question

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

Answer 1

Answer:

(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