Question

Find out the quotient and the remainder when
$P\left(x\right)=x^3+4x^2-5x+6$ is divided by $g\left(x\right)=x+1$

Answer 1

$x+1)\stackrel{x^2+3x-8}{\overline{x^3+4x^2-5x+6}}$
$\underset{(-)}{x^3}\underset{(-)}{+}1x^2$
$+3x^2-5x+6$
$\underset{(-)}{+}3x^2\underset{(-)}{+}3x$
$-8x+6$
$\underset{(+)}{8}x\underset{(+)}{-}8$
$14$
Therefore, $q\left(x\right)=x^2+3x-8$ and $R\left(x\right)=14$.