Question

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in the following case:

p(x) = 2x³ + x² – 2x – 1, g(x) = x + 1

Answer 1

If g(x) = x + 1 is a factor of the given polynomial p(x), then p(−1) must be zero.

p(x) = 2x³ + x² − 2x − 1

p(−1) = 2(−1)³ + (−1)² − 2(−1) − 1

= 2(−1) + 1 + 2 − 1

= 0

Hence, g(x) = x + 1 is a factor of the given polynomial.