Question

synthetic division
factor out a root:
$x^3+x^2-2$
1
use the optional scratchpad.
enter the result.

Explanation:

Step1: Set up synthetic division

Use root $x=1$, coefficients: $1, 1, 0, -2$

$$\begin{array}{r|rrrr} 1 & 1 & 1 & 0 & -2 \\ & & 1 & 2 & 2 \\ \hline & 1 & 2 & 2 & 0 \end{array}$$

Step2: Write factored polynomial

Quotient: $x^2+2x+2$, root factor: $(x-1)$

Answer:

$(x-1)(x^2+2x+2)$