Question
Write the correct answer in the following: $x + 1$ is a factor of the polynomial.
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Answer
Let assume $(x + 1)$ is a factor of $x^3 + x^2 + x + 1$
So$, x = -1$ is zero of $x^3 + x^2 + x + 1$
$(-1)^3 + (-1)^2 + (-1) + 1 = 0$
$\Rightarrow -1 + 1 - 1 + 1 = 0$
$\Rightarrow 0 = 0$
Hence, our assumption is true.
So$, x = -1$ is zero of $x^3 + x^2 + x + 1$
$(-1)^3 + (-1)^2 + (-1) + 1 = 0$
$\Rightarrow -1 + 1 - 1 + 1 = 0$
$\Rightarrow 0 = 0$
Hence, our assumption is true.
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