Answer
Quotient: $4x^{2}-11x+23$
remainder: $-45.$
Work Step by Step
$\begin{array}{llllll}
& 4x^{2} & -11x & +23 & & \\
& -- & -- & -- & -- & \\
x+2 \ \ &\left.\right) 4x^{3} & -3x^{2} & +x & +1 & \\
& 4x^{3} & +8x^{2} & & & \\
& -- & -- & & & \\
& & -11x^{2} & +x & & \\
& & -11x & -22x & & \\
& & -- & -- & & \\
& & & 23x & +1 & \\
& & & 23x & +46 & \\
& & & -- & -- & \\
& & & & -45 & \\
& & & & &
\end{array}$
Check:
$(x+2)\left(4x^{2}-11x+23\right)+(-45)$
$=4x^{3}-11x^{2}+23x+8x^{2}-22x+46-45$
$=4x^{3}-3x^{2}+x+1$
