Question

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

p(x) = x³ − 4x² + x + 6, g(x) = x − 3

Answer 1

If g(x) = x − 3 is a factor of the given polynomial p(x), then p(3) must be 0.

p(x) = x³ − 4x² + x + 6

p(3) = (3)³ − 4(3)² + 3 + 6

= 27 − 4(9) + 3 + 6

= 27 − 36 + 3 + 6

= 0

Hence, g(x) = x − 3 is a factor of the given polynomial.