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

(x4 − 3x² + 2 ) : (x − 3)

1

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

2

Set the coefficients of the dividend in one line.

3

In 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:

8

The last number obtained, 56, is the remainder.

9

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

x³ + 3 x² + 6x +18

Example

Divide by Ruffini's rule:

(x5 − 32) : (x − 2)

C(x) = x4 + 2x³ + 4x² + 8x + 16

R = 0

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Emma

I am passionate about travelling and currently live and work in Paris. I like to spend my time reading, gardening, running, learning languages and exploring new places.

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