Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], follow these steps:
1. Substitute -5 into the function: Replace every instance of [tex]\( x \)[/tex] in the equation with [tex]\(-5\)[/tex].
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- [tex]\((-5)^2\)[/tex] means multiplying [tex]\(-5\)[/tex] by itself, which equals [tex]\(25\)[/tex].
- [tex]\(-2(-5)\)[/tex] means multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex], equaling [tex]\(10\)[/tex].
- The constant term [tex]\(-7\)[/tex] remains as it is.
3. Combine the results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Add the values together:
- First add [tex]\(25\)[/tex] and [tex]\(10\)[/tex] to get [tex]\(35\)[/tex].
- Then subtract [tex]\(7\)[/tex] from [tex]\(35\)[/tex], which gives you [tex]\(28\)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is [tex]\( \boxed{28} \)[/tex].
1. Substitute -5 into the function: Replace every instance of [tex]\( x \)[/tex] in the equation with [tex]\(-5\)[/tex].
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- [tex]\((-5)^2\)[/tex] means multiplying [tex]\(-5\)[/tex] by itself, which equals [tex]\(25\)[/tex].
- [tex]\(-2(-5)\)[/tex] means multiply [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex], equaling [tex]\(10\)[/tex].
- The constant term [tex]\(-7\)[/tex] remains as it is.
3. Combine the results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Add the values together:
- First add [tex]\(25\)[/tex] and [tex]\(10\)[/tex] to get [tex]\(35\)[/tex].
- Then subtract [tex]\(7\)[/tex] from [tex]\(35\)[/tex], which gives you [tex]\(28\)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
The correct answer is [tex]\( \boxed{28} \)[/tex].
