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If [tex]P(x) = x^2 - 5x + 1[/tex], find [tex]P(2)[/tex] and [tex]P(-1)[/tex].

Hence, find [tex]P(2) + P(-1)[/tex].

Sagot :

GinnyAnswer
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]
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