Question

By using factor theorem in the following example, determine whether q(x) is a factor p(x) or not.

p(x) = x³ − x² − x − 1, q(x) = x − 1

Answer 1

p(x) = x³ − x² − x − 1

Divisor = q(x) = x − 1

∴ p(1) = (1)³ - (1)² − 1 − 1

= 1 − 1 − 1 − 1

= − 2 ≠ 0

Since p(1) ≠ 0, so by factor theorem q(x) = x − 1 is not a factor of polynomial p(x) = x³ − x² − x − 1.