Sum

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

x^{4} + 3x^{3} + 3x^{2} + x + 1

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#### Solution

If (x + 1) is a factor of polynomial p(x) = x^{4} + 3x^{3} + 3x^{2} + 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.

Concept: Concept of Polynomials

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