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Practical Briot-Ruffini Device


To effect the division of a polynomial P (x) by a binomial of the form (x -), we can use the practical Briot-Ruffini device.

Let's do the division of per x - 2through that device. Follow the roadmap for the resolution:

1º) We place the root of the divisor and the dividend coefficients (neatly from the highest grade term to the lowest grade term, filling in zero terms that do not appear) on the device:

2º) We lower the first dividend coefficient:

3º) We multiply the divisor root by the repeated coefficient and add the product to the second dividend coefficient, placing the result below it:

4º) We multiply the root of the divisor by the number below the 2nd coefficient and add the product with the 3rd coefficient, placing the result below it, and so on:

5º) We make a dash between the last and second to last numbers obtained. The last number is the same as the rest of the division, and the numbers to the left of it are the quotient coefficients:

Therefore,

Example

Get the quotient and the rest of the division of x³ - 3x² + 5x - 1 per 2x - 1:

Resolution

We have:
To apply the Briot-Ruffini device, the coefficient of x in the divider should be 1. In this case, we use the following device:

We do :

Applying Briot-Ruffini Device:

How :

Therefore, and .

Next: Successive Divisions