Answer
The quotient is $0.1x-0.21$
and the remainder is $0.241$.
Work Step by Step
The given expression is:-
$(0.1x^2-0.2)\div (x+2.1)$
Rewrite as descending powers of $x$.
$(0.1x^2+0x-0.2)\div (x+2.1)$
The divisor is $x+2.1$, so the value of $c=-2.1$.
and on the right side the coefficients of dividend in descending powers of $x$.
Perform synthetic division to obtain:
$\begin{matrix}
&-- &-- &--&& \\
-2.1) &0.1&0&-0.2&&&& \\
& &-0.21 &0.441 & & &\\
& -- & -- & --& &&& \\
& 0.1 & -0.21 & 0.241 & & &&\\
\end{matrix}$
The divisor is $x+2.1$
The dividend is $0.1x^2-0.2x$
The Quotient is $0.1x-0.21$
The remainder is $0.241$.
Check:-
$\text{(Divisor)(Quotient)+Remainder}$
$=(x+2.1)(0.1x-0.21)+0.241$
$=0.1x^2+0.21x-0.21x-0.441+0.241$
$=0.1x^3-0.2x$
Hence, the quotient is $0.1x-0.21$ and the remainder is $0.241$.
