Answer
See the explanation.
Work Step by Step
Synthetic Division,
To divide a polynomial by $x-c$,
1. Arrange the polynomial in descending powers, with a $0$ coefficient for missing terms
2.Write $c$ for the divisor, $x-c$. To the right, write the coefficient of the dividend
3.Write the leading coefficient of the dividend on the bottom row
4.Multiply $c$ times the value just written on the bottom row. Write the product in the next coloumn in the second row
5.Add the values in this new coloumn writing the sum in the bottom row
6.Repeat this series of multiplication. and addition until all coloumns are filled in.
7.Use the numbers in the last row to write the quotient plus the remainder above the divisor. The degree of the first term of the quotient is one less than the degree of the first term of this dividend. The final values in this row is the remainder
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Example:
$\begin{array}{lllll}
\underline{3}| & 2 & -3 & -11 & 7 \\
& & 6 & 9 &-6 \\
\hline & & & & \\
& 2 & 3 & -2 & 1
\end{array}$
$(2x^{3}-3x^2-11x+7)\div(x-3)=2x^2+3x-2+1/(x-3)$
