Answer
$-12$.
Work Step by Step
The given expression is
$\Rightarrow (20x^3+23x^2-10x+k)\div (4x+3)$
$\begin{matrix}
& 5x^2 & +2x &-4 & & \leftarrow &Quotient\\
&-- &-- &--&--& \\
4x+3) &20x^3&+23x^2&-10x&+k & \\
& 20x^3 & +15x^2 & & & \leftarrow &5x^2(4x+3) \\
& -- & -- & & & \leftarrow &subtract \\
& 0 & 8x^2 & -10x & & \\
& & 8x^2 & 6x & & \leftarrow & 2x(4x+3) \\
& & -- & -- & & \leftarrow & subtract \\
& & 0&-16x &+k& \\
& & & -16x& -12 & \leftarrow & -4(4x+3) \\
& & & -- & -- & \leftarrow & subtract \\
& & & 0 & 0 & \leftarrow & Remainder
\end{matrix}$
From the above calculations, $k$=$-12$.
