To find the expression that is equal to [tex]\( f(x) + g(x) \)[/tex], we should start by writing down the given functions and then combining them.
1. Write down the given functions:
[tex]\[
f(x) = -3x^2 + 4x + 4
\][/tex]
[tex]\[
g(x) = x(-7x - 7)
\][/tex]
2. Simplify [tex]\( g(x) \)[/tex]:
[tex]\[
g(x) = -7x^2 - 7x
\][/tex]
3. Add [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[
f(x) + g(x) = (-3x^2 + 4x + 4) + (-7x^2 - 7x)
\][/tex]
4. Combine like terms:
[tex]\[
f(x) + g(x) = -3x^2 - 7x^2 + 4x - 7x + 4
\][/tex]
[tex]\[
f(x) + g(x) = (-3x^2 - 7x^2) + (4x - 7x) + 4
\][/tex]
[tex]\[
f(x) + g(x) = -10x^2 - 3x + 4
\][/tex]
Therefore, the correct answer is:
[tex]\[
\boxed{D. \, -10 x^2 - 3 x + 4}
\][/tex]
