dividing polynomials

[mollykins]

I understand how to divide polynomials, but don't understand how or why it works, when using the bus shelter method (I think there's another way, but we haven't been taught it yet.)

Can anyone shed some light on why you end up with the right answer? Especially after you've moved everything down and taken things away from each other etc etc.

[bibblebub]

Stephen Hawking just been on the phone offering offering to nominate me for the Nobel prize for physics.

[mollykins]

Thanks factor.

one of the things we did in the lesson was (x^3-3x^2-x-3) divided by (x-1). I got the answer as x^2-2x-3 but don't understand why it works.

[mibn2cweus]

wooden it be x^2-2x-four?

[vascop]

There's something wrong there Molly because if you multiply (x-1) and( x^2-2x-3) together then you should get x^3-3x^2-x-3, but you don't you get +3 at the end instead of -3. Another way of looking at it is that if your answer was right then x=1 would be a root of the original polynomial (cubic), but it isnt (try substituting x=1 and you don't get 0).
I think it should be +3 at the end. and than your answer would be right.

[mibn2cweus]

No . . . your answer was right.
In the first term I subtracted the x first then the 3 instead of subtracting the 3 from x first and subtracting the difference so for the first time OOO is (x^3-3x^2-[x-3]).

[mollykins]

I've just looked in my book and yes it should be +3, sorry.

I know that you'd times the answer by x+1 to get the other bit, but I don't understand why it works.

[vascop]

Notice that x^2-2x-3=(x-3)(x+1). So the whole thing x^3-3x^2-x+3=(x-1)(x+1)(x-3)
So if you divide by any of those 3 factors (x-1),(x+1), or (x-3) you should get the product of the other 2 as the answer. Try it out.

[mibn2cweus]

Think I'll just go check out the yard sales.

[vascop]

Bus shelter method:
x^2 - 2x - 3
======================
x+1|x^3 - 3x^2 - x + 3
x^3 - x^2
- 2x^2 - x
- 2x^2 + 2x
- 3x + 3
- 3x + 3

This is just long division used for polynomials, and it works because multiplying each term of the answer by (x-1):
x^2(x-1)-2x(x-1)-3(x-1) gives x^3-3x^2-x+3

[Buenchico]

One of the problems of using calculators in classrooms is that primary school children either aren't taught 'long division' or forget how to use it.

Take a look at this page about good old-fashioned basic (numerical) long division and make sure that you can understand what's going on:
http://www.mathsonline.org/pages/longdiv.html

Then compare it with what's on this page:
http://www.purplemath.com/modules/polydiv2.htm

You should be able to see that you're doing nothing different to what you probably did (however briefly) in primary school.

Chris

[mike11111]

I am in my early 60s and although I am very familiar with long division (both arithmetical and algebraic) I have never come across the expression "bus shelter method".

[Answerprancer]

...looks like she's got you there then Mike11111 ;-)

[Buenchico]

Don't worry about it, Mike.

I taught maths (to GCSE and A-level) for 15 years and I'd not heard of it either ;-)

[mrs_overall]

At school I was familiar with the Bike Shed method, if that's any use?

[Mamyalynne]

Mike it could be that we were taught in the multi storey car park method?

[mike11111]

Yeah, you're right. Anyway, must nip out and buy her a birthday present.

[scotman]

I am quite old but I have not heard of 'the bus shelter method' either. I do vaguely remember something at uni called 'synthetic division'. Is that similar?

[vascop]

If you want us to explain what bus shelter method means and compare it with what you were taught at uni, then you;ve got to tell us what this synthetic divisionmethod was, or have you forgotten? If so then why mention it?

[mike11111]

I assume that it is named thus because the long bracket enclosing the dividend looks like a child's drawing of a bus shelter.

[scotman]

Is this any help

http://en.wikipedia.o...ynomial_long_division

or this

http://www.purplemath.com/modules/polydiv2.htm