Which of the following expressions is equivalent to 6x^2 - 15x - 36 and is factored comple… — Armed Services Vocational Aptitude Battery (ASVAB)

Which of the following expressions is equivalent to $6x^2 - 15x - 36$ and is factored completely?

The completely factored expression is

3(2x + 3)(x - 4)

The correct answer identifies the GCF of 3 and correctly factors the remaining quadratic

2x^2 - 5x - 12

into

(2x + 3)(x - 4)

. Expanding this result confirms it equals

6x^2 - 15x - 36

and no further factors can be extracted.

Identify and factor out the greatest common factor (GCF) from all three terms.

3(2x^2 - 5x - 12)

The coefficients 6, -15, and -36 are all divisible by 3.

Find two numbers that multiply to

ac

(where

a=2

and

c=-12

, so

2 \times -12 = -24

) and add to the middle coefficient (

b=-5

The numbers are

-8

and

3

(-8) \times 3 = -24

and

(-8) + 3 = -5

Rewrite the trinomial by splitting the middle term using these two numbers.

3(2x^2 - 8x + 3x - 12)

This sets up the polynomial for factoring by grouping.

Factor the trinomial by grouping.

3[2x(x - 4) + 3(x - 4)] = 3(2x + 3)(x - 4)

Factoring out

(x - 4)

from both groups provides the final completely factored form.

Factoring out a GCF followed by factoring a non-monic trinomial.

Question