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Question
Determine the following polynomial has (x + 1) a factor:
x3 + x2 + x + 1
Solution
If (x + 1) is a factor of p(x) = x3 + x2 + x + 1, then p (−1) must be zero, otherwise (x + 1) is not a factor of p(x).
p(x) = x3 + x2 + x + 1
p(−1) = (−1)3 + (−1)2 + (−1) + 1
= − 1 + 1 − 1 + 1
= 0
Hence, x + 1 is a factor of this polynomial.
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