Answer
$Q(x)= \displaystyle \frac{1}{2}x^{3}-x^{2}-\frac{5}{2}x-\frac{7}{4},\quad R(x)=\frac{19}{2}x+1$
Work Step by Step
$\left[\begin{array}{l}
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4x^{2}-6x+8\ )\\
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\end{array}\right. \left.\begin{array}{llllll}
\frac{1}{2}x^{3} & -x^{2} & -\frac{5}{2}x & -\frac{7}{4} & & \\
\hline 2x^{5} & -7x^{4} & & & & -13\\
2x^{5} & -3x^{4} & +4x^{3} & & & \\
-- & -- & -- & & & \\
& -4x^{4} & -4x^{3} & & & -13\\
& -4x^{4} & +6x^{3} & -8x^{2} & & \\
& -- & -- & -- & & \\
& & -10x^{3} & +8x^{2} & & -13\\
& & -10x^{3} & +15x^{2} & -20x & \\
& & -- & -- & -- & \\
& & & -7x^{2} & +20x & -13\\
& & & -7x^{2} & -\frac{21}{2}x & -14\\
& & & -- & -- & --\\
& & & & \frac{19}{2}x & +1
\end{array}\right]$
$Q(x)= \displaystyle \frac{1}{2}x^{3}-x^{2}-\frac{5}{2}x-\frac{7}{4},\quad R(x)=\frac{19}{2}x+1$
