# Chapter One - Algebra and Functions - Dividing by Polynomials

A worked example of a question envolving dividing by polynomials. Includes questions to test yourself, worked answers, colour coding and - get this - a SMILEY FACE!

Hope it's useful - please remember to comment on it! Thank you!!

- Created by: Maddison
- Created on: 23-05-09 16:22

First 215 words of the document:

DIVIDING A POLYNOMIAL BY (x ± p)

3 3

The question: "Divide x + 6x + 8x + 3 by ( x + 1) "

Ok, I think the best way to tackle this is to explain by example...:

Essentially, what you're doing is taking away terms to get to zero.

Explaining the colours:

Black and pink is the original sum bit

To work out what to divide the pink bit by, you divide the first term of the polynomial by x. (The

highlighted yellow thing).

Pale blue is the first step:

o You multiply (x + 1) by x2 to give x3 + x2 . You then take this away from

x3 + 6x2 + 8x + 3

This gives you 5x2 . You then bring down the 8x to give you 5x2 + 8x

o Multiply (x + 1) by 5x to give you 5x2 + 5x. As before, you then take

this away from 5x2 + 8x...

To give 3x. Bring down the 3, and this gives you 3x + 3.

o Multiply (x + 1) by 3 to give 3x + 3. Take it away, and you get 0.

AND YOU'RE DONE!

Your final answer is the bit that's at the top of the bar thingy, and is called the

quotient.

Be warned they're gunna get harder.

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