Answer
Quotient $=-3x^3-3x^2-3x-5$
Remainder $=-6$
Work Step by Step
The given expression is
$(-3x^4-2x-1)\div(x-1)$
Rewrite the expression as
$(-3x^4+0x^3+0x^2-2x-1)\div(x-1)$
Perform long division:
$\begin{matrix}
& -3x^3 & -3x^2 & -3 x&-5 &&& \leftarrow &\text{Quotient}\\
&-- &-- &--&--& \\
x-1) &-3x^4&+0x^3&+0x^2&-2x&-1 & \\
&-3x^4 & +3x^3& &&&& \leftarrow &-3x^3(x-1) \\
& -- & --& &&&&\leftarrow &\text{subtract} \\
& 0 & -3x^3& 0x^2 & & & \\
& &-3x^3 & +3x^2& &&& \leftarrow &-3x^2(x-1) \\
& & -- & --& &&&\leftarrow &\text{subtract} \\
& & 0 & -3x^2& -2x & & & \\
& &&-3x^2 & +3x&& & \leftarrow &-3x(x-1) \\
& && -- & --& &&\leftarrow &\text{subtract} \\
& && 0 & -5x & -1 & & \\
& &&&-5x & +5& & \leftarrow &-5(x-1) \\
& &&& -- & --& &\leftarrow &\text{subtract} \\
& && & 0 & -6 & &
\leftarrow & \text{Remainder}
\end{matrix}$
Checking:
$\text{(Quotient)(divisor)+ Remainder}$
$=(-3x^3-3x^2-3x-5)(x-1)-6$
$=-3x^4-3x^3-3x^2-5x+3x^3+3x^2+3x+5-6$
$=-3x^4-2x-1$
$=\text{ Dividend}$
Hence, the quotient is $-3x^3-3x^2-3x-5$ and the remainder is $-6$.
