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] into the function in place of [tex]\( x \)[/tex]. Here is a step-by-step explanation:
1. Start with the polynomial function:
[tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the equation:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate each part of the expression:
- First, square [tex]\(-5\)[/tex]:
[tex]\((-5)^2 = 25\)[/tex].
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\( -2 \times (-5) = 10 \)[/tex].
- Finally, combine these results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Add and subtract the numbers:
[tex]\[
F(-5) = 25 + 10 - 7 = 28
\][/tex]
Therefore, the value of [tex]\( F(-5) \)[/tex] is [tex]\(\boxed{28}\)[/tex].
1. Start with the polynomial function:
[tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the equation:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate each part of the expression:
- First, square [tex]\(-5\)[/tex]:
[tex]\((-5)^2 = 25\)[/tex].
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\( -2 \times (-5) = 10 \)[/tex].
- Finally, combine these results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Add and subtract the numbers:
[tex]\[
F(-5) = 25 + 10 - 7 = 28
\][/tex]
Therefore, the value of [tex]\( F(-5) \)[/tex] is [tex]\(\boxed{28}\)[/tex].
