Check whether $x + 1$ is a factor of $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$ .

True

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False

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Solution

The correct option is B False
The zero of $x + 1$ is $- 1$
Let $p (x) = x^{4} + 3 x^{3} + 3 x^{2} + x + 1$
Then, $p (- 1) = (- 1)^{4} + 3 (- 1)^{3} + 3 (- 1)^{2} + (- 1) + 1$
$= 1 - 3 + 3 - 1 + 1 = 1$
Since, $p (- 1) \neq 0$
Therefore, by Factor theorem, $x + 1$ is not a factor of $x^{4} + 3 x^{3} + 3 x^{2} + x + 1$

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