Determine which of the following polynomials has (x + 1) a factor: x⁴ + x³ + x² + x + 1

(ii) Let p(x) = x⁴ + x³ + x² + x + 1
Putting x + 1 = 0, we get, x = -1
Using remainder theorem, when p(x) = x⁴ + x³ + x² + x + 1 is divided by x 1, reminder is given by p(-1)
= (-1)⁴ + (-1)³ + (-1)² + (-1) + 1
= 1 – 1 + 1 – 1 + 1
= 1
Since, reminder p(-1) ≠0, hence x + 1 is not a factor of x⁴ + x³ + x² + x + 1.

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