Answer
$ 16x^2 -8x+4-\frac{2}{2x+1}$
Work Step by Step
The given expression is
$(64x^3+4)\div(4x+2)$
Rewrite the expression as
$(64x^3+0x^2+0x+4)\div(4x+2)$
$\begin{matrix}
& 16x^2 & -8x &+4 & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
4x+2) &64x^3&+0x^2&+0x&+4 & \\
& 64x^3 & +32x^2 & & & \leftarrow &16x^2(4x+2) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & -32x^2 & +0x & & \\
& & -32x^2 & -16x & & \leftarrow & -8x(4x+2) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&16x &+4 & \\
& & & 16x& +8 & \leftarrow & 4(4x+2) \\
& & & -- & -- & \leftarrow & subtract \\
& & & 0 & -4 & \leftarrow & Remainder
\end{matrix}$
The answer is
$\Rightarrow Quotient + \frac{Remainder}{Divisor}$
$\Rightarrow 16x^2 -8x+4-\frac{4}{4x+2}$
Factor out $2$ from the denominator.
$\Rightarrow 16x^2 -8x+4-\frac{4}{2(2x+1)}$
Simplify.
$\Rightarrow 16x^2 -8x+4-\frac{2}{2x+1}$.
