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!

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  • Created by: Maddison
  • Created on: 23-05-09 16:22
Preview of Chapter One - Algebra and Functions - Dividing by Polynomials

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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.
Your final answer is the bit that's at the top of the bar thingy, and is called the
Be warned they're gunna get harder.

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Sometimes, you'll get numbers leftover at the end ­ i.e. you won't get zero at
the end.
Also, you'll probably have to divide by x minus something ­ in which case,
you'll have to be aware of whether you multiply the polynomial by a positive or
a negative number.…read more

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