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