Question

which expressions are equivalent to $6x^{2}+3x - 9$?
select two correct answers.
$3(2x + 3)(x - 1)$
$3(2x^{2}+x - 3)$
$-3(2x - 3)(x - 1)$
$3(2x - 3)(x + 1)$
$-3(2x^{2}+x + 3)$
clear all

Explanation:

Step1: Factor out common term

Factor 3 from the original expression:
$6x^2 + 3x - 9 = 3(2x^2 + x - 3)$

Step2: Factor the quadratic

Factor $2x^2 + x - 3$ into binomials:
$2x^2 + x - 3 = (2x + 3)(x - 1)$
Substitute back to get:
$3(2x + 3)(x - 1)$

Step3: Verify other options

Check if other forms match. Expand $-3(2x - 3)(x - 1)$:
$-3(2x^2 - 5x + 3) = -6x^2 + 15x - 9$, which does not match.
Expand $3(2x - 3)(x + 1)$:
$3(2x^2 - x - 3) = 6x^2 - 3x - 9$, which does not match.
Expand $-3(2x^2 + x + 3)$:
$-6x^2 - 3x - 9$, which does not match.

Answer:

A. $3(2x + 3)(x - 1)$
B. $3(2x^2 + x - 3)$