Question

factor the following trinomial.
$2x^2 + 5x - 12$
select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. $2x^2 + 5x - 12 = \square$
b. the polynomial is prime.

Explanation:

Step1: Split middle term

Find two numbers: product $2\times(-12)=-24$, sum $5$. The numbers are $8$ and $-3$.
$2x^2 + 8x - 3x - 12$

Step2: Group and factor pairs

Group first/second, third/fourth terms.
$(2x^2 + 8x) + (-3x - 12) = 2x(x+4) - 3(x+4)$

Step3: Factor out common binomial

Extract $(x+4)$ from both terms.
$(2x - 3)(x + 4)$

Answer:

A. $2x^{2}+5x-12=(2x-3)(x+4)$