What are the factors of 2x^2 + 5x - 12?

(2x - 3) • (x + 4)

Step-by-step explanation:

Step 1:

Equation at step 1:

(2x2 + 5x) - 12

Step 2:

Trying to factor by splitting the middle term

2.1 Factoring 2x2+5x-12

The first term is, 2x2 its coefficient is 2.

The middle term is, + 5x its coefficient is 5.

The last term, "the constant", is - 12

Step-1 : Multiply the coefficient of the first term by the constant 2 • - 12 = - 24

Step-2 : Find two factors of - 24 whose sum equals the coefficient of the middle term, which is 5.

-24 + 1 = - 23

-12 + 2 = - 10

-8 + 3 = - 5

-6 + 4 = - 2

-4 + 6 = 2

-3 + 8 = 5

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 3 and 8

2x2 - 3x + 8x - 12

Step-4 : Add up the first 2 terms, pulling out like factors:

x • (2x-3)

Add up the last 2 terms, pulling out common factors:

4 • (2x-3)

Step-5 : Add up the four terms of step 4:

(x+4) • (2x-3)

Which is the desired factorization