To determine which expression is equivalent to the given expression [tex]\( -2x^2 + 8x - 9 + 4x + 7x^2 + 2 \)[/tex], we will simplify it step by step:
1. Combine the like terms involving [tex]\( x^2 \)[/tex]:
[tex]\[
-2x^2 + 7x^2 = 5x^2
\][/tex]
2. Combine the like terms involving [tex]\( x \)[/tex]:
[tex]\[
8x + 4x = 12x
\][/tex]
3. Combine the constant terms:
[tex]\[
-9 + 2 = -7
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[
5x^2 + 12x - 7
\][/tex]
Thus, the given expression simplifies to [tex]\( 5x^2 + 12x - 7 \)[/tex].
Correct Answer: A. [tex]\( 5x^2 + 12x - 7 \)[/tex]
