a student factors 3x² - 12 to the following. 3(x² - 4) which statement about 3(x² - 4) is true? the…

Explanation:

Step1: Check equivalence

We start with the original expression $3x^{2}-12$. Factoring out the greatest - common factor 3, we get $3(x^{2}-4)$. Since $3x^{2}-12 = 3\times x^{2}-3\times4=3(x^{2}-4)$ by the distributive property $a(b + c)=ab+ac$ (here $a = 3$, $b=x^{2}$, $c=-4$), the expression $3(x^{2}-4)$ is equivalent to $3x^{2}-12$.

Step2: Check if completely factored

The expression $x^{2}-4$ is a difference of squares. The formula for factoring a difference of squares is $a^{2}-b^{2}=(a + b)(a - b)$. Here, $a = x$ and $b = 2$, so $x^{2}-4=(x + 2)(x - 2)$. Thus, $3(x^{2}-4)$ is not completely factored.

Answer:

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