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 function in place of [tex]\( x \)[/tex].
Here's how to do it step-by-step:
1. Substitute [tex]\(-5\)[/tex] into the function:
We replace every occurrence of [tex]\( x \)[/tex] with [tex]\(-5\)[/tex], so it becomes:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- First, calculate [tex]\((-5)^2\)[/tex]:
[tex]\((-5)^2 = 25\)[/tex]
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\(-2 \times (-5) = 10\)[/tex]
- The constant term is [tex]\(-7\)[/tex].
3. Combine all the terms:
Now, add the results together:
[tex]\[
25 + 10 - 7
\][/tex]
4. Perform the addition and subtraction:
- First, add [tex]\(25\)[/tex] and [tex]\(10\)[/tex]:
[tex]\(25 + 10 = 35\)[/tex]
- Then, subtract [tex]\(7\)[/tex] from [tex]\(35\)[/tex]:
[tex]\(35 - 7 = 28\)[/tex]
So, [tex]\( F(-5) = 28 \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{28}\)[/tex].
Here's how to do it step-by-step:
1. Substitute [tex]\(-5\)[/tex] into the function:
We replace every occurrence of [tex]\( x \)[/tex] with [tex]\(-5\)[/tex], so it becomes:
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- First, calculate [tex]\((-5)^2\)[/tex]:
[tex]\((-5)^2 = 25\)[/tex]
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]:
[tex]\(-2 \times (-5) = 10\)[/tex]
- The constant term is [tex]\(-7\)[/tex].
3. Combine all the terms:
Now, add the results together:
[tex]\[
25 + 10 - 7
\][/tex]
4. Perform the addition and subtraction:
- First, add [tex]\(25\)[/tex] and [tex]\(10\)[/tex]:
[tex]\(25 + 10 = 35\)[/tex]
- Then, subtract [tex]\(7\)[/tex] from [tex]\(35\)[/tex]:
[tex]\(35 - 7 = 28\)[/tex]
So, [tex]\( F(-5) = 28 \)[/tex].
Therefore, the correct answer is [tex]\(\boxed{28}\)[/tex].
