Let's solve the problem step-by-step.
Given the polynomial function:
[tex]\[ P(x) = x^2 - 5x + 1 \][/tex]
1. Find [tex]\( P(2) \)[/tex]
Substitute [tex]\( x = 2 \)[/tex] into the polynomial:
[tex]\[
P(2) = 2^2 - 5(2) + 1
\][/tex]
Simplify the expression step-by-step:
[tex]\[
P(2) = 4 - 10 + 1
\][/tex]
[tex]\[
P(2) = -6 + 1
\][/tex]
[tex]\[
P(2) = -5
\][/tex]
Therefore, [tex]\( P(2) = -5 \)[/tex].
2. Find [tex]\( P(-1) \)[/tex]
Substitute [tex]\( x = -1 \)[/tex] into the polynomial:
[tex]\[
P(-1) = (-1)^2 - 5(-1) + 1
\][/tex]
Simplify the expression step-by-step:
[tex]\[
P(-1) = 1 + 5 + 1
\][/tex]
[tex]\[
P(-1) = 7
\][/tex]
Therefore, [tex]\( P(-1) = 7 \)[/tex].
3. Find [tex]\( P(2) + P(-1) \)[/tex]
Now, we add the values of [tex]\( P(2) \)[/tex] and [tex]\( P(-1) \)[/tex]:
[tex]\[
P(2) + P(-1) = -5 + 7
\][/tex]
Simplify the expression:
[tex]\[
P(2) + P(-1) = 2
\][/tex]
Therefore, the final answers are:
[tex]\[ P(2) = -5 \][/tex]
[tex]\[ P(-1) = 7 \][/tex]
[tex]\[ P(2) + P(-1) = 2 \][/tex]
