Answer :
Sure! Let's find [tex]\( F(-5) \)[/tex] for the given polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
To find [tex]\( F(-5) \)[/tex], we need to substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the polynomial and solve:
1. Start with the given function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate each term:
- [tex]\((-5)^2 = 25\)[/tex]
- [tex]\(-2(-5) = 10\)[/tex]
- Combine these with [tex]\(-7\)[/tex]:
[tex]\[
25 + 10 - 7
\][/tex]
4. Add these values together:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
5. So, [tex]\( F(-5) = 28 \)[/tex].
Thus, the correct answer is [tex]\( \boxed{28} \)[/tex].
To find [tex]\( F(-5) \)[/tex], we need to substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the polynomial and solve:
1. Start with the given function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate each term:
- [tex]\((-5)^2 = 25\)[/tex]
- [tex]\(-2(-5) = 10\)[/tex]
- Combine these with [tex]\(-7\)[/tex]:
[tex]\[
25 + 10 - 7
\][/tex]
4. Add these values together:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
5. So, [tex]\( F(-5) = 28 \)[/tex].
Thus, the correct answer is [tex]\( \boxed{28} \)[/tex].
