Question

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

p(x) = x³ + 3x² + 3x + 1, g(x) = x + 2

Answer 1

If g(x) = x + 2 is a factor of the given polynomial p(x), then p(−2) must be 0.

p(x) = x³ + 3x² + 3x + 1

p(−2) = (−2)³ + 3(−2)² + 3(−2) + 1

= − 8 + 12 − 6 + 1

= −1

As p(−2) ≠ 0,

Hence, g(x) = x + 2 is not a factor of the given polynomial.