#### Answer

$q(x)=2x^{2}+x+6$
$r(x)=-38$

#### Work Step by Step

1. Arrange the terms...
2. Divide the first term in the dividend by the first term in the divisor.
The result is the first term of the quotient.
3. Multiply every term in the divisor by the first term in the quotient.
Write the resulting product beneath the dividend with like terms lined up.
4. Subtract the product from the dividend.
5. Bring down the next term in the original dividend and write it next to the
remainder to form a new dividend.
6. repeat steps $3-5$ until the remainder can no longer be divided.
----------------
$\begin{array}{llllll}
& & 2x^{2} & +x & +6 & -\frac{38}{x+3}\\
& -- & --- & --- & --- & \\
x+3\ \ ) & 2x^{3} & +7x^{2} & +9x & -20 & \\
& 2x^{3} & +6x^{2} & & & \\
& -- & --- & & & \\
& & x^{2} & +9x & & \\
& & x^{2} & +3x & & \\
& & --- & --- & & \\
& & & 6x & -20 & \\
& & & 6x & +18 & \\
& & & --- & --- & \\
& & & & -38 &
\end{array}$
$q(x)=2x^{2}+x+6$
$r(x)=-38$