Answer
The quotient is $x^2+x-4$ and the remainder is $5$.
Work Step by Step
The given expression is:-
$(x^3+2x^2-3x+1)\div (x+1)$
The divisor is $x+1$, so the value of $c=-1$.
and on the right side the coefficients of dividend in descending powers of $x$.
$\begin{matrix}
&-- &-- &--&--& \\
-1) &1&2&-3&1& & \\
& &-1 &-1 &4 && \\
& -- & -- & --& -- && \\
& 1 & 1& -4 &5 & \\
\end{matrix}$
The Quotient is $x^2+x-4$
The remainder is $5$.
Check:-
$=\text{(Divisor)(Quotient)+Remainder}$
$=(x+1)(x^2+x-4)+5$
$=x^3+x^2-4x+x^2+x-4+5$
$=x^3+2x^2-3x+1$
Hence, the quotient is $x^2+x-4$ and the remainder is $5$.
