Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial function [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], we'll substitute [tex]\( x = -5 \)[/tex] into the function and evaluate it step by step.
1. Start with the given function:
[tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\( F(-5) = (-5)^2 - 2(-5) - 7 \)[/tex].
3. Calculate each term:
- The first term is [tex]\( (-5)^2 \)[/tex]. When you square [tex]\(-5\)[/tex], you get [tex]\( 25 \)[/tex].
- The second term is [tex]\( -2(-5) \)[/tex]. Multiplying [tex]\(-2\)[/tex] and [tex]\(-5\)[/tex] gives [tex]\( 10 \)[/tex].
- The third term is [tex]\(-7\)[/tex].
4. Add the results:
[tex]\( 25 + 10 - 7 \)[/tex].
5. Perform the addition and subtraction:
First add [tex]\( 25 + 10 = 35 \)[/tex].
Then subtract [tex]\( 7 \)[/tex] from [tex]\( 35 \)[/tex] to get [tex]\( 28 \)[/tex].
Thus, the value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex]. So, the correct answer is option C: 28.
1. Start with the given function:
[tex]\( F(x) = x^2 - 2x - 7 \)[/tex].
2. Substitute [tex]\( x = -5 \)[/tex] into the function:
[tex]\( F(-5) = (-5)^2 - 2(-5) - 7 \)[/tex].
3. Calculate each term:
- The first term is [tex]\( (-5)^2 \)[/tex]. When you square [tex]\(-5\)[/tex], you get [tex]\( 25 \)[/tex].
- The second term is [tex]\( -2(-5) \)[/tex]. Multiplying [tex]\(-2\)[/tex] and [tex]\(-5\)[/tex] gives [tex]\( 10 \)[/tex].
- The third term is [tex]\(-7\)[/tex].
4. Add the results:
[tex]\( 25 + 10 - 7 \)[/tex].
5. Perform the addition and subtraction:
First add [tex]\( 25 + 10 = 35 \)[/tex].
Then subtract [tex]\( 7 \)[/tex] from [tex]\( 35 \)[/tex] to get [tex]\( 28 \)[/tex].
Thus, the value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex]. So, the correct answer is option C: 28.
