Answer
Quotient $=-4x^2-3x-3$
Remainder $=-7$
Work Step by Step
The given expression is
$(-4x^3+x^2-4)\div(x-1)$
Rewrite the expression as
$(-4x^3+x^2+0x-4)\div(x-1)$
Perform long division:
$\begin{matrix}
& -4x^2 & -3x & -3 & && \leftarrow &\text{Quotient}\\
&-- &-- &--&--& \\
x-1) &-4x^3&+x^2&+0x&-4 & \\
&-4x^3 & +4x^2& &&& \leftarrow &-4x^2(x-1) \\
& -- & --& &&&\leftarrow &\text{subtract} \\
& 0 & -3x^2& 0x & & & \\
& &-3x^2 & +3x& && \leftarrow &-3x(x-1) \\
& & -- & --& &&\leftarrow &\text{subtract} \\
& & 0 & -3x& -4 & & & \\
& &&-3x & +3& & \leftarrow &-3(x-1) \\
& && -- & --& &\leftarrow &\text{subtract} \\
& && 0 & -7 & & \leftarrow & \text{Remainder}
\end{matrix}$
Checking:
$\text{(Quotient)(divisor)+ Remainder}$
$=(-4x^2-3x-3)(x-1)-7$
$=-4x^3-3x^2-3x+4x^2+3x+3-7$
$=-4x^3+x^2-4$
$=\text{Dividend}$
Hence, the quotient is $-4x^2-3x-3$ and the remainder is $-7$.
