The polynomial 8*x*2 – 8*x* + 2 – 5 + *x* is simplified to 8*x*2 – *gx* – *h*. What are the value of *g* and *h*?

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.

Learn how to simplify the polynomial 8x^2 - 8x + 2 - 5 + x with a step-by-step guide. This problem covers key algebraic concepts, including combining like terms and simplifying polynomials. Suitable for students in Grades 7-9.

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