Answer :
To find [tex]\( F(-5) \)[/tex] for the polynomial [tex]\( F(x) = x^2 - 2x - 7 \)[/tex], follow these steps:
1. Substitute [tex]\(-5\)[/tex] for [tex]\(x\)[/tex]: Replace every [tex]\(x\)[/tex] in the polynomial with [tex]\(-5\)[/tex].
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- First, calculate [tex]\((-5)^2\)[/tex]. Remember that multiplying two negative numbers results in a positive number:
[tex]\[
(-5)^2 = 25
\][/tex]
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]. A negative times a negative is positive:
[tex]\[
-2 \times (-5) = 10
\][/tex]
- The last term is [tex]\(-7\)[/tex], which remains the same.
3. Combine the results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Perform the arithmetic:
- 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]
The value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex].
Therefore, the correct answer is C. 28.
1. Substitute [tex]\(-5\)[/tex] for [tex]\(x\)[/tex]: Replace every [tex]\(x\)[/tex] in the polynomial with [tex]\(-5\)[/tex].
[tex]\[
F(-5) = (-5)^2 - 2(-5) - 7
\][/tex]
2. Calculate each term:
- First, calculate [tex]\((-5)^2\)[/tex]. Remember that multiplying two negative numbers results in a positive number:
[tex]\[
(-5)^2 = 25
\][/tex]
- Next, calculate [tex]\(-2 \times (-5)\)[/tex]. A negative times a negative is positive:
[tex]\[
-2 \times (-5) = 10
\][/tex]
- The last term is [tex]\(-7\)[/tex], which remains the same.
3. Combine the results:
[tex]\[
F(-5) = 25 + 10 - 7
\][/tex]
4. Perform the arithmetic:
- 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]
The value of [tex]\( F(-5) \)[/tex] is [tex]\( 28 \)[/tex].
Therefore, the correct answer is C. 28.
