Answer:
The expression is not equivalent, and it is not completely factored.
Step-by-step explanation:
Given expression:
[tex]3x^4-12[/tex]
Student factors it to [tex]3(x^2-4)[/tex]
to choose the correct statement about the student's answer.
Solution.
We will completely factor the given expression.
We have,
[tex]3x^4-12[/tex]
Factoring out 3 which is the greatest common factor for both terms
⇒ [tex]3(x^4-4)[/tex]
Factoring the difference of squares [[tex]a^2-b^2=(a+b)(a-b)[/tex] ]
⇒ [tex]3((x^2)^2-2^2)[/tex]
⇒ [tex]3(x^2+2)(x^2-2)[/tex]
⇒ [tex]3(x^2+2)(x^2-(\sqrt2)^2)[/tex]
⇒ [tex]3(x^2+2)(x+\sqrt2)(x-\sqrt2)[/tex] [Further difference of squares]
From the steps we see that none of the steps are equivalent to the student's expression.
Thus, we can say that the expression is not equivalent, and it is not completely factored.
