Question
Determine which of the following polynomials has (x + 1) a factor:
x4 + x3 + x2 + x + 1
Solution
x4 + x3 + x2 + x + 1
Let p(x) = x4 + x3 + x2 + x + 1
The zero of x + 1 is - 1.
p(- 1) = (- 1)4 + (- 1)3 + (- 1)2 + (- 1) + 1
= 1 - 1 + 1 - 1 + 1 = 1 ≠ 0
∴ By factor theorem, x + 1 is not a factor of x4 + x3 + x2 + x + 1.
