# Determine which of the following polynomials has (x + 1) a factor: x^4 + 3x^3 + 3x^2 + x + 1

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Determine which of the following polynomials has (x + 1) a factor:

x4 + 3x3 + 3x2 + x + 1

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If (x + 1) is a factor of polynomial p(x) = x4 + 3x3 + 3x2 + x + 1, then p(−1) must be 0, otherwise (x + 1) is not a factor of this polynomial.

p(−1) = (−1)4 + 3(−1)3 + 3(−1)2 + (−1) + 1

= 1 − 3 + 3 − 1 + 1 = 1 As p(−1) ≠ 0,

Therefore, x + 1 is not a factor of this polynomial.

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