Answer
The quotient is $0.1x^2-0.11x+0.321$
and the remainder is $-0.3531$.
Work Step by Step
The given expression is:-
$(0.1x^3+0.2x)\div (x+1.1)$
Rewrite as descending powers of $x$.
$(0.1x^3+0x^2+0.2x+0)\div (x+1.1)$
The divisor is $x+1.1$, so the value of $c=-1.1$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&--& \\
-1.1) &0.1&0&0.2&0&&& \\
& &-0.11 &0.121 &-0.3531 & &\\
& -- & -- & --& -- &&& \\
& 0.1 & -0.11 & 0.321 &-0.3531 & &&\\
\end{matrix}$
The divisor is $x+1.1$
The dividend is $0.1x^3+0.2x$
The Quotient is $0.1x^2-0.11x+0.321$
The remainder is $-0.3531$.
Check:-
$\text{(Divisor)(Quotient)+Remainder}$
$=(x+1.1)(0.1x^2-0.11x+0.321)-0.3531$
$=0.1x^3-0.11x^2+0.321x+0.11x^2-0.121x+0.3531-0.3531$
$=0.1x^3+0.2x$
Hence, the quotient is $0.1x^2-0.11x+0.321$ and the remainder is $-0.3531$.
