To solve for the values of $g$ and $h$, let's simplify the given polynomial step by step.

The given polynomial is: $8x^2 - 8x + 2 - 5 + x$

First, let's combine like terms:

1. The $x^2$ term: $8x^2$ (no other $x^2$ terms to combine).
2. The $x$ terms: $-8x + x = -7x$.
3. The constant terms: $2 - 5 = -3$.

So, the simplified polynomial is: $8x^2 - 7x - 3$

We are told that the simplified form is $8x^2 - gx - h$.

By comparing the coefficients, we can see that:

• $g = 7$
• $h = 3$

Therefore, the correct values are: $g = 7 \quad \text{and} \quad h = 3$

The correct answer is:

• $g = 7$ and $h = 3$

Would you like more details, or do you have any questions? Here are 5 related questions you might find interesting:

1. How do you simplify polynomials with more variables?
2. What is the significance of the leading coefficient in a polynomial?
3. How do you factor quadratic polynomials?
4. What is the difference between polynomial expressions and polynomial functions?
5. How do you find the roots of a quadratic polynomial?

Tip: When combining like terms in a polynomial, always carefully match the powers of $x$ (or other variables) to ensure accurate simplification.