Question

a student factors $3x^2 - 12$ to the following.
$3(x^2 - 4)$
which statement about $3(x^2 - 4)$ is true?
○ the expression is equivalent, and it is completely factored.
○ the expression is equivalent, but it is not completely factored.
○ the expression is not equivalent, but it is completely factored.
○ the expression is not equivalent, and it is not completely factored.

Explanation:

Step1: Check equivalence

Factor out 3 from $3x^2 - 12$:
$3x^2 - 12 = 3(x^2 - 4)$, so the expressions are equivalent.

Step2: Check complete factorization

Notice $x^2 - 4$ is a difference of squares, which factors as $(x+2)(x-2)$. So $3(x^2 - 4)$ can be further factored to $3(x+2)(x-2)$, meaning it is not completely factored.

Answer:

The expression is equivalent, but it is not completely factored.