$${ x }^{ 3 } + { x }^{ 2 } +ax+x+a+1$$
$\left(x+1\right)\left(x^{2}+a+1\right)$
$$x\left(x^{2}+a+1\right)+x^{2}+a+1$$
$$\left(x^{2}+a+1\right)\left(x+1\right)$$
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