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ahleelee
 Post subject: Pls help me with this,thx
PostPosted: 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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Shadow
 Post subject: Re: Pls help me with this,thx
PostPosted: Mon, 4 Jun 2012 13:51:16 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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ahleelee
 Post subject: Re: Pls help me with this,thx
PostPosted: Mon, 4 Jun 2012 14:11:20 UTC 
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Shadow,can you make in more detailed,or shall I find the f(x) first.
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Shadow
 Post subject: Re: Pls help me with this,thx
PostPosted: 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 {f(x)\over (x-1)(x+2)} is equal to f(x) times the partial fraction decomposition of {1\over (x-1)(x+2)} and you can use that to solve for f(x).

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outermeasure
 Post subject: Re: Pls help me with this,thx
PostPosted: Mon, 4 Jun 2012 14:22:17 UTC 
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Shadow 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.


??? :confused:

Factor theorem alone suffices.

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\begin{aligned} Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\ Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\ Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\ Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\ Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\ Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4 \end{aligned}
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Shadow
 Post subject: Re: Pls help me with this,thx
PostPosted: Mon, 4 Jun 2012 15:56:20 UTC 
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outermeasure wrote:
Shadow 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.


??? :confused:

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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ahleelee
 Post subject: Re: Pls help me with this,thx
PostPosted: Mon, 4 Jun 2012 16:09:39 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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Shadow
 Post subject: Re: Pls help me with this,thx
PostPosted: 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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alstat
 Post subject: Re: Pls help me with this,thx
PostPosted: Tue, 5 Jun 2012 00:41:43 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.

I assume f(x) is a polynomial function.

If so, you need to know that when f(x) leaves a remainder of r when divided by (x - a), that means
f(x) = p(x)(x - a) + r for some function p(x)

AND it also means that f(a) = r.

So f(x) = p(x)(x - 1) + 1 for some p(x).

Also, f(-2) = -3.

So now, find p(-2) and use that to express p(x) in terms of some function q(x).

Then you can express f(x) in terms of q(x) and you will be done.

Spoiler:
You should get p(-2) = \frac{4}{3}

so that p(x) = q(x)(x + 2) + \frac{4}{3}

and f(x) = q(x)(x + 2)(x - 1) + \frac{4}{3}(x - 1) + 1 = ...
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Shadow
 Post subject: Re: Pls help me with this,thx
PostPosted: Tue, 5 Jun 2012 01:04:31 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 f(x) 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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ahleelee
 Post subject: Re: Pls help me with this,thx
PostPosted: Tue, 5 Jun 2012 03:12:26 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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