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*?

*g* = –9 and *h* = 7

*g* = 9 and *h* = –3

*g* = –7 and *h* = 7

*g* = 7 and *h* = 3

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.

Learn how to simplify the polynomial 8x^2 - 8x + 2 - 5 + x step-by-step. Understand how to combine like terms and compare coefficients to find values of g and h. Suitable for high school students learning algebraic simplification.

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