Determine which of the following polynomials has $(x + 1)$ a factor :
$x^{3} + x^{2} + x + 1$

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Solution

We have,
$x^{3} + x^{2} + x + 1$
Apply remainder theorem.
$x + 1 = 0$
$x = - 1$
Replace x by $- 1$ we get
$= x^{3} + x^{2} + x + 1$
$= (- 1)^{3} + (- 1)^{2} + (- 1) + 1$
$= - 1 + 1 - 1 + 1$
$= 0$
Hence, this is answer.

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