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

Question

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

Philoid · Accepted Answer

We know that (x – 1) will be the factor of the polynomial if by substituting x = 1 in polynomial we get the zero remainder.

∴ by putting x = 1 in x⁴ + x³ + x² + x + 1, we get -

1⁴ + 1³ + 1² + 1 + 1 = 5≠0

⇒ (x – 1) is not a factor of x⁴ + x³ + x² + x + 1.