To simplify the given polynomial $8x^2 - 8x + 2 - 5 + x$, we can combine like terms. Here's how it's done step by step:

Step 1: Combine the $x$ terms

The terms involving $x$ are: $-8x + x = -7x$

Step 2: Combine the constant terms

The constant terms are: $2 - 5 = -3$

Step 3: Write the simplified polynomial

After combining the terms, the simplified polynomial is: $8x^2 - 7x - 3$

Step 4: Match the simplified polynomial with the given form

The simplified polynomial $8x^2 - 7x - 3$ corresponds to the form $8x^2 - gx - h$.

So, we have:

• $g = 7$
• $h = 3$

Final Answer:

• $g = 7$
• $h = 3$

Would you like more details on the process, or do you have any questions?

Here are 5 related questions you might find helpful:

1. How do you factor a quadratic expression like $8x^2 - 7x - 3$?
2. What is the significance of the leading coefficient in a quadratic equation?
3. Can the value of $g$ be negative in other polynomial problems?
4. How does combining like terms help in simplifying polynomials?
5. What is the next step after simplifying a polynomial for solving it?

Tip: Always combine like terms in a polynomial to simplify it before attempting further operations like factoring or solving.