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Select the correct answer.

Consider functions [tex]f[/tex] and [tex]g[/tex].
[tex]\[
\begin{array}{l}
f(x) = -3x^2 + 4x + 4 \\
g(x) = x(-7x - 7)
\end{array}
\][/tex]

Which expression is equal to [tex]f(x) + g(x)[/tex]?

A. [tex]-3x^2 - 3x - 3[/tex]

B. [tex]4x^2 - 3x + 4[/tex]

C. [tex]-10x^2 + 4x - 3[/tex]

D. [tex]-10x^2 - 3x + 4[/tex]



Answer :

GinnyAnswer
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]

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