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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
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Solution
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.
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