Question

A student factors 3x2 – 12 to the following. 3(x2 – 4)

Answer 1

So, the factors of 3x² – 12 are 3(x-2)(x+2).

Explanation:

We have given expression:

3x² – 12

We have to find the factor of the given expression.

First, taking 3 common from the expression we get,

3x² – 12=3(x²-4)

As we know that,

a²-b²= (a-b)(a+b)

Then we get,

3x² – 12= 3(x-2)(x+2)

So, the factors of 3x² – 12 are 3(x-2)(x+2).

Answer 2

The expression is equivalent , but is not completely factored

Explanation:

A student factors 3x² – 12 to the following. 3(x² – 4)

3x² – 12 is equivalent to 3(x² – 4), because 3 was factored out;

If we multiply by 3 by opening the brackets then we get the same expression 3x² – 12.

However; 3(x² – 4), could be factored further;

To get; 3(x + 2)(x - 2) ; since x² – 4 is a difference of two squares;

Therefore;

3x² – 12 = 3(x² – 4) = 3(x + 2)(x - 2)