Let's simplify the polynomial [tex]\(8x^2 - 8x + 2 - 5 + x\)[/tex] step by step.
1. Combine like terms for [tex]\(x\)[/tex]-terms:
[tex]\[
-8x + x = -7x
\][/tex]
2. Combine constant terms:
[tex]\[
2 - 5 = -3
\][/tex]
Now, let's rewrite the polynomial with the simplified terms:
[tex]\[
8x^2 - 7x - 3
\][/tex]
We need to match this simplified polynomial to the form [tex]\(8x^2 - gx - h\)[/tex].
From the simplified polynomial:
[tex]\[
g = 7, \quad h = 3
\][/tex]
However, in the problem [tex]\(g\)[/tex] is given as a negated value, so we need to account for that:
[tex]\[
g = -7
\][/tex]
Therefore, the correct values are [tex]\(g = -7\)[/tex] and [tex]\(h = 3\)[/tex].
The correct answer in our list is:
[tex]\[
g = -7 \quad \text{and} \quad h = 3
\][/tex]
Thus, the correct choice is:
[tex]\[
g = -7 \quad \text{and} \quad h = 3
\][/tex]
