To simplify the given expression and find the equivalent expression among the given choices, follow these steps:
Given expression:
[tex]\[
-2 x^2 + 8 x - 9 + 4 x + 7 x^2 + 2
\][/tex]
1. Combine like terms:
- First, combine all the [tex]\(x^2\)[/tex] terms:
[tex]\[
-2x^2 + 7x^2 = (7 - 2)x^2 = 5x^2
\][/tex]
- Next, combine all the [tex]\(x\)[/tex] terms:
[tex]\[
8x + 4x = (8 + 4)x = 12x
\][/tex]
- Finally, combine the constant terms:
[tex]\[
-9 + 2 = -7
\][/tex]
2. Summarize the simplified expression:
[tex]\[
5x^2 + 12x - 7
\][/tex]
Now, let's examine the choices provided and see which one matches our simplified expression:
A. [tex]\(-5x^2 + 4x + 11\)[/tex] — this does not match.
B. [tex]\(-9x^2 + 4x - 7\)[/tex] — this does not match.
C. [tex]\(5x^2 + 12x - 7\)[/tex] — this is exactly what we obtained.
D. [tex]\(-9x^2 - 12x + 11\)[/tex] — this does not match.
Thus, the correct answer is:
[tex]\[
\boxed{C}
\][/tex]
