To subtract the polynomials [tex]\( \left(6 f^2 - 9 f + 10\right) \)[/tex] and [tex]\( \left(-2 f^2 - f + 3\right) \)[/tex], we follow these steps:
1. Write down the polynomials:
[tex]\[
(6 f^2 - 9 f + 10) - (-2 f^2 - f + 3)
\][/tex]
2. Distribute the negative sign across the second polynomial:
[tex]\[
6 f^2 - 9 f + 10 + 2 f^2 + f - 3
\][/tex]
3. Combine like terms:
- For [tex]\( f^2 \)[/tex] terms:
[tex]\[
6 f^2 + 2 f^2 = 8 f^2
\][/tex]
- For [tex]\( f \)[/tex] terms:
[tex]\[
-9 f + f = -8 f
\][/tex]
- For constant terms:
[tex]\[
10 - 3 = 7
\][/tex]
4. Put it all together:
[tex]\[
8 f^2 - 8 f + 7
\][/tex]
So, the result of subtracting [tex]\( \left(6 f^2 - 9 f + 10\right) - \left(-2 f^2 - f + 3\right) \)[/tex] is:
[tex]\[
\boxed{8 f^2 - 8 f + 7}
\][/tex]
Among the given choices, [tex]\( 8 f^2 - 8 f + 7 \)[/tex] is the correct answer.
