To determine which polynomial represents the sum of the given polynomials
[tex]\[
\left(16 x^2 - 16 \right) + \left( -12 x^2 - 12 x + 12 \right),
\][/tex]
we need to combine like terms from each polynomial.
1. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
16x^2 + (-12x^2) = 16x^2 - 12x^2 = 4x^2
\][/tex]
2. Combine the [tex]\(x\)[/tex] terms:
The first polynomial does not have an [tex]\(x\)[/tex] term, so we take the [tex]\(x\)[/tex] term from the second polynomial:
[tex]\[
-12x
\][/tex]
3. Combine the constant terms:
[tex]\[
-16 + 12 = -4
\][/tex]
Putting it all together, the sum of the polynomials is:
[tex]\[
4x^2 - 12x - 4
\][/tex]
Thus, the correct polynomial representing the sum is:
[tex]\[
\boxed{4x^2 - 12x - 4}
\][/tex]
So the answer is:
[tex]\[
\text{B. } 4 x^2 - 12 x - 4
\][/tex]
