Answer :
To find [tex]\(F(-5)\)[/tex] for the polynomial function [tex]\(F(x) = x^2 - 2x - 7\)[/tex], follow these steps:
1. Start by substituting [tex]\(x = -5\)[/tex] into the polynomial [tex]\(F(x)\)[/tex].
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Then, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Finally, substitute these values into the polynomial:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Simplify the expression by adding and subtracting the numbers:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
So, [tex]\(F(-5) = 28\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{28}
\][/tex]
1. Start by substituting [tex]\(x = -5\)[/tex] into the polynomial [tex]\(F(x)\)[/tex].
2. Calculate [tex]\((-5)^2\)[/tex]:
[tex]\[
(-5)^2 = 25
\][/tex]
3. Then, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\[
-2 \times (-5) = 10
\][/tex]
4. Finally, substitute these values into the polynomial:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
5. Simplify the expression by adding and subtracting the numbers:
[tex]\[
25 + 10 = 35
\][/tex]
[tex]\[
35 - 7 = 28
\][/tex]
So, [tex]\(F(-5) = 28\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{28}
\][/tex]
