The polynomial \( 8x^2 - 8x + 2 - 5 + x \) is simplified to \( 8x^2 - gx - h \). What are the values of \( g \) and \( h \)?

A. \( g = -9 \) and \( h = 7 \)
B. \( g = 9 \) and \( h = -3 \)
C. \( g = -7 \) and \( h = 7 \)
D. [tex]\( g = 7 \)[/tex] and [tex]\( h = 3 \)[/tex]



Answer :

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]