Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases: (i) p(x) = 2x^3 + x^2 − 2x − 1, g(x) = x + 1
Use the Factor Theorem to determine whether g(x) is a factor of p(x) in each of the following cases:
(i) p(x) = 2x3 + x2 − 2x − 1, g(x) = x + 1
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(i) If g(x) = x + 1 is a factor of the given polynomial p(x), then p(−1) must be zero.
p(x) = 2x3 + x2 − 2x − 1
p(−1) = 2(−1)3 + (−1)2 − 2(−1) − 1
= 2(−1) + 1 + 2 − 1 = 0
Hence, g(x) = x + 1 is a factor of the given polynomial.
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