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Answer :
To find [tex]\( F(-5) \)[/tex] for the given polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], we need to substitute [tex]\( -5 \)[/tex] in place of [tex]\( x \)[/tex] in the function. Here's how you can do it step-by-step:
1. Substitute [tex]\( x = -5 \)[/tex] into the function [tex]\( F(x) \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate the square of [tex]\(-5\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Plug-in these values into the expression:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Add and subtract the numbers to find the final value:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
Therefore, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is D. 28.
1. Substitute [tex]\( x = -5 \)[/tex] into the function [tex]\( F(x) \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate the square of [tex]\(-5\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Plug-in these values into the expression:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Add and subtract the numbers to find the final value:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
Therefore, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is D. 28.
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