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Question
Determine the following polynomial has (x + 1) a factor:
x4 + x3 + x2 + x + 1
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Solution
If (x + 1) is a factor of p(x) = x4 + x3 + x2 + x + 1, then p (−1) must be zero, as a result (x + 1) is not a factor of p(x).
p(x) = x4 + x3 + x2 + x + 1
p(−1) = (−1)4 + (−1)3 + (−1)2 + (−1) + 1
= 1 − 1 + 1 − 1 + 1
= 1
As p(−1) ≠ 0,
Therefore, x + 1 is not a factor of this polynomial.
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