To find the values of [tex]\( g \)[/tex] and [tex]\( h \)[/tex] in the polynomial expression [tex]\( 8x^2 - gx - h \)[/tex], let's simplify the given polynomial step-by-step.
We start with the polynomial:
[tex]\[ 8x^2 - 8x + 2 - 5 + x \][/tex]
1. Combine the like terms. Keep the [tex]\( x^2 \)[/tex] terms, [tex]\( x \)[/tex] terms, and constant terms separate:
[tex]\[ 8x^2 - 8x + x + 2 - 5 \][/tex]
2. Simplify the [tex]\( x \)[/tex] terms:
[tex]\[ 8x^2 - 7x + 2 - 5 \][/tex]
3. Simplify the constant terms:
[tex]\[ 8x^2 - 7x - 3 \][/tex]
Now we compare this simplified form, [tex]\( 8x^2 - 7x - 3 \)[/tex], with the polynomial [tex]\( 8x^2 - gx - h \)[/tex].
From the comparison, we can see that:
[tex]\[ g = 7 \][/tex]
[tex]\[ h = 3 \][/tex]
So, the correct values of [tex]\( g \)[/tex] and [tex]\( h \)[/tex] are:
[tex]\[ g = 7 \][/tex]
[tex]\[ h = 3 \][/tex]
Therefore, the correct choice is:
[tex]\[ g = 7 \text{ and } h = 3 \][/tex]
