# Ruffini's Rule

In order to explain the steps to implement Ruffini's rule, an example division will be used throughout the explaination:

(x^{4} − 3x^{2} + 2 ) : (x − 3)

1 If the polynomial is not complete, complete it by adding the missing terms with zeros.

2Set the coefficients of the dividend in one line.

3In the bottom left, place the opposite of the independent term of the divisor.

4 Draw a line and lower the first coefficient.

5 Multiply this coefficient by the divisor and place it under the following term.

6 Add the two coefficients.

7 Repeat the process above.

Repeat the process:

Repeat, again:

8The last number obtained, 56, is the remainder.

9The quotient is a polynomial of lower degree and whose coefficients are the ones obtained in the division.

x^{3} + 3 x^{2} + 6x +18

#### Example

Divide by Ruffini's rule:

(x^{5} − 32) : (x − 2)

C(x) = x^{4} + 2x^{3} + 4x^{2} + 8x + 16

R = 0