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 Post subject: Pls help me with this,thxPosted: Mon, 4 Jun 2012 13:30:14 UTC
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The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 13:51:16 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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ahleelee wrote:
The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

Do partial fractions.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 14:11:20 UTC
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Joined: Mon, 4 Jun 2012 07:44:06 UTC
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Shadow,can you make in more detailed,or shall I find the f(x) first.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 14:21:53 UTC
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ahleelee wrote:
Shadow,can you make in more detailed,or shall I find the f(x) first.

The trick is you know that is equal to times the partial fraction decomposition of and you can use that to solve for f(x).

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 14:22:17 UTC
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ahleelee wrote:
The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

Do partial fractions.

???

Factor theorem alone suffices.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 15:56:20 UTC
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outermeasure wrote:
ahleelee wrote:
The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

Do partial fractions.

???

Factor theorem alone suffices.

Yes, but I thought this was cute, and the op didn't give any indications as to his background, so I threw it out there.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 16:09:39 UTC
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Joined: Mon, 4 Jun 2012 07:44:06 UTC
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Dear two,I'm trying hard to work it out with your hints.
I know it won,t be soon.

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 Post subject: Re: Pls help me with this,thxPosted: Mon, 4 Jun 2012 19:29:26 UTC
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ahleelee wrote:
Dear two,I'm trying hard to work it out with your hints.
I know it won,t be soon.

If you get stuck after a while, try posting what you tried and we can try and look it over.

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 Post subject: Re: Pls help me with this,thxPosted: Tue, 5 Jun 2012 00:41:43 UTC
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Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 278
Location: Chandler, AZ, USA
ahleelee wrote:
The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

I assume is a polynomial function.

If so, you need to know that when leaves a remainder of r when divided by , that means
for some function

AND it also means that .

So for some .

Also, .

So now, find and use that to express in terms of some function .

Then you can express in terms of and you will be done.

Spoiler:
You should get

so that

and

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 Post subject: Re: Pls help me with this,thxPosted: Tue, 5 Jun 2012 01:04:31 UTC
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Joined: Wed, 30 Mar 2005 04:25:14 UTC
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alstat wrote:
ahleelee wrote:
The remainder is 1 when f(x) is devided by x-1,-3 when devided by x+2; and Ax+B when devided (x-1)(x+2),find A and B.

I assume is a polynomial function.

Why are you assuming that? It falls out of the work you do.

And you are trying to say f(x) is that based on a couple of values? LaGrange interpolation would give infinitely many things satisfying that.

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 Post subject: Re: Pls help me with this,thxPosted: Tue, 5 Jun 2012 03:12:26 UTC
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Joined: Mon, 4 Jun 2012 07:44:06 UTC
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I failed to succeed by using the partial fraction for hours.
I found little in 1/(x-1)(x-2),so I turned to factor theorem.
I put x=1 and x=-2 respectively into
f(x)-(x-1)(x+2)Q(x)=Ax+B
I got A=4/3 and B=-1/3
I don't know correct or not since I don't have f(x) to verify with.
I eager to know The method using partial fraction.

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