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