Question

the area of a rectangle is a = 36x^{2}-24x square inches. what are three different possible
select all that apply.
a. 6x inches by 6x - 4 inches
b. 3x inches by 12x - 9 inches
c. 8x inches by 4x - 3 inches
d. 2x inches by 18x - 12 inches
e. 4x inches by 9x - 6 inches

Explanation:

Step1: Factor the area expression

Factor $36x^{2}-24x$. We can take out the greatest - common factor $12x$, so $36x^{2}-24x = 12x(3x - 2)$. We can also factor it in other ways by splitting the common - factor differently.
$36x^{2}-24x=2x(18x - 12)$ (taking out $2x$), and $36x^{2}-24x = 4x(9x - 6)$.

Step2: Check each option

Option A:

Multiply $6x(6x - 4)=36x^{2}-24x$.

Option B:

Multiply $3x(12x - 9)=36x^{2}-27x
eq36x^{2}-24x$.

Option C:

Multiply $8x(4x - 3)=32x^{2}-24x
eq36x^{2}-24x$.

Option D:

Multiply $2x(18x - 12)=36x^{2}-24x$.

Option E:

Multiply $4x(9x - 6)=36x^{2}-24x$.

Answer:

A. 6x inches by 6x - 4 inches
D. 2x inches by 18x - 12 inches
E. 4x inches by 9x - 6 inches