Math Is Fun Forum

austin81

Member

Registered: 2005-03-21

Posts: 39

Prob on Polynomials

When a polynomial is divided by x-3, the remainder is 3 and when it is divided by x+2, the remainder is 13. Find the remainder when it is divided by(x-3)(x+2)> Hence write out the polynomial.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Prob on Polynomials

Hi austin81;

The polynomial is only a linear one. 9 - 2x is the polynomial that leaves a remainder of 3 and 13. When it is divided by (x-3)(x+2) then 9 - 2x is the remainder of course.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Prob on Polynomials

Hi

I assumed P(x) was a cubic and found an infinite number of possibilities!  Here's one:

!

This has a remainder of -2x +9 when divided by the quadratic (x-3)(x+2).  But I worked it this way round.  I don't know how to get the remainder first then the polynomial.

Any cubic of the form

should work.

I think!

I'll re-consider if someone can tell me how to get the third remainder, just from the other two.  Thanks.

Bob

ps.  Maybe I should assume the remainder must be a number without x???

pps  bobbym.  If you put a = b = 0 my general cubic becomes your answer.

Last edited by Bob (2010-10-24 03:03:47)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Prob on Polynomials

Hi Bob;

That is why I went with the linear one. Generally you try for the smallest order. The linear one is unique, higher orders will not be. You cannot determine a higher unique answer because the poster has not told us what remainder is left when the poly is divided by (x+2)(x-3). I am not even sure he wants to divide by that.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Prob on Polynomials

hi bobbym,

I'm working on a post for the suggestions slot which is intended to encourage posters to give more information when asking for help.  It's a long post and I'm only half way through constructing it.  Please look out for it and let me know what you think.

Best wishes,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Prob on Polynomials

That is a good idea. How will you get people to read it?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,623

Re: Prob on Polynomials

Hi bobbym,

I've just completed it and put it on the suggestions page.

How to get people to read it?

You ask the toughest puzzles don't you!

I'd have big letters and a pretty graphic on the front page and maybe more graphics to support each point.

Plus, we'd have a reasonable excuse to respond "Please read the front page advice before continuing!."

You could make a macro to do that automatically at the touch of a button!:)

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Prob on Polynomials

You have my support and help but it does depend on MIF. It is his time that really is the question. All those are good ideas up there.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.