Question

If $x^3+x^2+x+a$ is divisible by $x-1$, find the value of $a$.

Answer 1

Determine the value of $a$.

Let $p\left(x\right)=x^3+x^2+x+a$

If $\left(x-1\right)$ is a factor of $p\left(x\right)$, then $p\left(1\right)=0$.

$\begin{array}{rcl}p\left(1\right)& =& 0\\ {\left(1\right)}^3+{\left(1\right)}^2+\left(1\right)+a& =& 0\\ 3+a& =& 0\\ a& =& -3\end{array}$

Hence, the value of $a$ is $-3$.