To simplify the polynomial \(8x^2 - 8x + 2 - 5 + x\) and find the values of \(g\) and \(h\) such that it takes the form \(8x^2 - gx - h\), follow these steps:
1. Rewrite the polynomial by grouping like terms:
\(8x^2 - 8x + 2 - 5 + x\)
2. Combine the terms with \(x\):
\(-8x + x = -7x\)
So far, we have: \(8x^2 - 7x\)
3. Combine the constant terms:
\(2 - 5 = -3\)
Now, the polynomial is \(8x^2 - 7x - 3\)
4. Compare the simplified polynomial with the given form \(8x^2 - gx - h\):
When we compare \(8x^2 - 7x - 3\) with \(8x^2 - gx - h\),
- The coefficient of \(x\) term is \(-7\), so \(g = 7\).
- The constant term is \(-3\), so \(h = 3\).
Thus, the correct values are:
[tex]\[ g = 7 \quad \text{and} \quad h = 3 \][/tex]
The correct option is:
[tex]\[ \boxed{g = 7 \text{ and } h = 3} \][/tex]
