Given the polynomial fx4x3x2x1 calculate f1 f1Solutionfx x4

Given the polynomial f=x^4+x^3+x^2+x+1 calculate f(1), f(-1)

Solution

f(x) = x^4+x^3+x^2+x+1 .

To find f(1) and f(-1).

To get f(1) , we put x = 1 in inthe expression. and evaluete the expression.

f(x) = x^4+x^3+x^2+x+1. Put x = 1and we get:

f(1) = 1^4+1^3+1^2+1+1 = 5

So f(1) = 5.

To get f(-1) , we put x = -1 in f(x) = x^4+x^3+x^2+x+1 and we get:

f(-1) = (-1)^4+(-1)^3+(-1)^2+(-1)+1

f(-1) = 1 -1 +1 -1+1 = 3-2 = 1.

So f(-1) = 1.

f(-1)