Use the Factor Theorem to determine whether g(x) is a factor of p(x) i

1.	Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2
Answer» 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.

Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:p(x) = x3 + 3x2 + 3x + 1, g(x) = x + 2

Answer»

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.