The rem function returns the remainder of a divided by b. The quo function returns the quotient of a divided by b. The remainder r and quotient q satisfy: $a=bq+r$  where $\mathrm{degree}\left(r\&comma;x\right)<\mathrm{degree}\left(b\&comma;x\right)$.

If a fourth argument is included in the calling sequence for rem or quo, it will be assigned the quotient q or remainder r, respectively.

$\mathrm{divide}\left(x^3+x+1\&comma;x^2+x+1\right)$

$\mathrm{false}$

$\mathrm{quo}\left(x^3+x+1\&comma;x^2+x+1\&comma;x\right)$

$x-1$

$\mathrm{r1}≔\mathrm{rem}\left(x^3+x+1\&comma;x^2+x+1\&comma;x\&comma;'\mathrm{q1}'\right)$

$\mathrm{r1}≔x+2$

$\mathrm{q1}$

$x-1$

$a≔\left(x^2+x+1\right)\mathrm{q1}+\mathrm{r1}$

$a≔\left(x^2+x+1\right)\left(x-1\right)+x+2$

$\mathrm{simplify}\left(a\right)$

$x^3+x+1$

$\mathrm{q2}≔\mathrm{quo}\left(x^4-3x+2\&comma;x^2-x-1\&comma;x\&comma;'\mathrm{r2}'\right)$

$\mathrm{q2}≔x^2+x+2$

$\mathrm{r2}$

$4$

$\mathrm{q2}+\frac{\mathrm{r2}}{x^2-x-1}$

$x^2+x+2+\frac{4}{x^2-x-1}$

$\mathrm{simplify}\left(\right)$

$\frac{x^4-3x+2}{x^2-x-1}$