Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], we need to substitute [tex]\(-5\)[/tex] in place of [tex]\( x \)[/tex] and evaluate the expression.
Here are the steps:
1. Substitute [tex]\(-5\)[/tex] into the polynomial:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Evaluate the expression by combining these results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Simplify the expression:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
Therefore, the value of [tex]\( F(-5) \)[/tex] is [tex]\(\boxed{28}\)[/tex].
Here are the steps:
1. Substitute [tex]\(-5\)[/tex] into the polynomial:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Evaluate the expression by combining these results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Simplify the expression:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
Therefore, the value of [tex]\( F(-5) \)[/tex] is [tex]\(\boxed{28}\)[/tex].