Answer :

To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], follow these steps:

1. Substitute [tex]\(-5\)[/tex] into the polynomial: Replace every occurrence of [tex]\( x \)[/tex] in the polynomial with [tex]\(-5\)[/tex].
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]

2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]

3. Calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]

4. Complete the calculation: Add the results from the previous steps together and then subtract 7.
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]

5. Simplify the expression:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]

Thus, [tex]\( F(-5) = 28 \)[/tex]. The correct answer is D. 28.

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