Sarthaks Test
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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

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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.

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