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Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], we substitute [tex]\(-5\)[/tex] into the polynomial for [tex]\( x \)[/tex].
Let's go through the steps:
1. Substitute [tex]\(-5\)[/tex] into the equation in place of [tex]\( x \)[/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. Put all these results into the original polynomial:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Now, add and subtract in the expression:
- First, add 25 and 10:
[tex]\[
25 + 10 = 35
\][/tex]
- Then subtract 7 from 35:
[tex]\[
35 - 7 = 28
\][/tex]
So, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is [tex]\( \boxed{28} \)[/tex].
Let's go through the steps:
1. Substitute [tex]\(-5\)[/tex] into the equation in place of [tex]\( x \)[/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. Put all these results into the original polynomial:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Now, add and subtract in the expression:
- First, add 25 and 10:
[tex]\[
25 + 10 = 35
\][/tex]
- Then subtract 7 from 35:
[tex]\[
35 - 7 = 28
\][/tex]
So, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is [tex]\( \boxed{28} \)[/tex].
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