Answer
The quotient is $-4x^2+10x-21$
and the remainder is $43$.
Work Step by Step
The given expression is:-
$(-4x^3+2x^2-x+1)\div (x+2)$
The divisor is $x+2$, so the value of $c=-2$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& \\
-2) &-4&2&-1&1& & \\
& &8 &-20 &42 && \\
& -- & -- & --& -- && \\
& -4 & 10 & -21 &43 & \\
\end{matrix}$
The divisor is $x+2$
The dividend is $-4x^3+2x^2-x+1$
The Quotient is $-4x^2+10x-21$
The remainder is $43$.
Check:-
$=\text{(Divisor)(Quotient)+Remainder}$
$=(x+2)(-4x^2+10x-21)+43$
$=-4x^3+10x^2-21x-8x^2+20x-42+43$
$=-4x^3+2x^2-x+1$
Hence, the quotient is $-4x^2+10x-21$ and the remainder is $43$.
