College

Given the polynomial function below, find [tex] F(-5) [/tex].

[tex] F(x) = x^2 - 2x - 7 [/tex]

A. -42
B. 28
C. 8
D. -22

Answer :

Sure! Let's solve the problem step-by-step:

We are given a polynomial function:

[tex]\[ F(x) = x^2 - 2x - 7 \][/tex]

We need to find the value of [tex]\( F(-5) \)[/tex].

To do this, we will substitute [tex]\( x = -5 \)[/tex] into the polynomial function and calculate:

1. Start with the expression:

[tex]\[ F(x) = x^2 - 2x - 7 \][/tex]

2. Substitute [tex]\(-5\)[/tex] for [tex]\(x\)[/tex]:

[tex]\[ F(-5) = (-5)^2 - 2(-5) - 7 \][/tex]

3. Calculate each part:

- [tex]\((-5)^2 = 25\)[/tex]
- [tex]\(-2(-5) = 10\)[/tex]

4. Substitute these values back into the expression:

[tex]\[ F(-5) = 25 + 10 - 7 \][/tex]

5. Simplify:

[tex]\[ F(-5) = 35 - 7 \][/tex]

6. Final calculation:

[tex]\[ F(-5) = 28\][/tex]

So, the value of [tex]\( F(-5) \)[/tex] is 28. The correct answer is B. 28.