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 − 4 x2 + x + 6, g(x) = x − 3

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

p(x) = x3 − 4 x2 + x + 6

p(3) = (3)3 − 4(3)2 + 3 + 6

= 27 − 36 + 9 = 0

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

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