Answer :
Sure! To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( f(x) = x^2 - 2x - 7 \)[/tex], we need to substitute [tex]\(-5\)[/tex] into the function for [tex]\( x \)[/tex] and simplify. Here’s how to do it step-by-step:
1. Start with the given function:
[tex]\( f(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the function:
[tex]\( f(-5) = (-5)^2 - 2(-5) - 7 \)[/tex].
3. Calculate each term:
- [tex]\((-5)^2\)[/tex] means you multiply [tex]\(-5\)[/tex] by itself, which gives [tex]\( 25 \)[/tex].
- [tex]\(-2(-5)\)[/tex] involves multiplying [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex], resulting in [tex]\( 10 \)[/tex].
- The constant [tex]\(-7\)[/tex] remains the same.
4. Put it all together:
[tex]\( f(-5) = 25 + 10 - 7 \)[/tex].
5. Simplify the expression:
- Add [tex]\( 25 \)[/tex] and [tex]\( 10 \)[/tex] to get [tex]\( 35 \)[/tex].
- Subtract [tex]\( 7 \)[/tex] from [tex]\( 35 \)[/tex], which equals [tex]\( 28 \)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
Looking at the options given:
- A. -42
- B. -22
- C. 28
- D. 8
The correct answer is C. 28.
1. Start with the given function:
[tex]\( f(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\(-5\)[/tex] for [tex]\( x \)[/tex] in the function:
[tex]\( f(-5) = (-5)^2 - 2(-5) - 7 \)[/tex].
3. Calculate each term:
- [tex]\((-5)^2\)[/tex] means you multiply [tex]\(-5\)[/tex] by itself, which gives [tex]\( 25 \)[/tex].
- [tex]\(-2(-5)\)[/tex] involves multiplying [tex]\(-2\)[/tex] by [tex]\(-5\)[/tex], resulting in [tex]\( 10 \)[/tex].
- The constant [tex]\(-7\)[/tex] remains the same.
4. Put it all together:
[tex]\( f(-5) = 25 + 10 - 7 \)[/tex].
5. Simplify the expression:
- Add [tex]\( 25 \)[/tex] and [tex]\( 10 \)[/tex] to get [tex]\( 35 \)[/tex].
- Subtract [tex]\( 7 \)[/tex] from [tex]\( 35 \)[/tex], which equals [tex]\( 28 \)[/tex].
Therefore, [tex]\( F(-5) = 28 \)[/tex].
Looking at the options given:
- A. -42
- B. -22
- C. 28
- D. 8
The correct answer is C. 28.
