Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], we substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the polynomial and evaluate it step-by-step:
1. Start with the polynomial [tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] into the expression for [tex]\( x \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
4. Calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
5. Now, substitute the results back into the expression:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
6. Perform the final addition and subtraction:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
So, the value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex]. Therefore, the correct answer is B. 28.
1. Start with the polynomial [tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] into the expression for [tex]\( x \)[/tex]:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
3. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
4. Calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
5. Now, substitute the results back into the expression:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
6. Perform the final addition and subtraction:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
So, the value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex]. Therefore, the correct answer is B. 28.
