Question

Determine if the following polynomial has (x + 1) a factor :-

x⁴ + x³ + x² + x + 1

Answer 1

If (x + 1) is a factor of p(x) = x⁴ + x³ + x² + x + 1, then p (−1) must be zero, otherwise (x + 1) is not a factor of p(x).

p(x) = x⁴ + x³ + x² + x + 1

p(−1) = (−1)⁴ + (−1)³ + (−1)² + (−1) + 1

         = 1 − 1 + 1 −1 + 1

         = 1

As p(− 1) ≠ 0,

Therefore, x + 1 is not a factor of this polynomial.