(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Applying remainder theorem again and again to show that the remainder of the f(x) polynomial function when divided by (x-α)(x-β) is A(x-α)+B . Determine A and B

2. Relevant equations

the remainder of a polynomial f(x), divided by a linear divisor x-a, is equal to f(a)

3. The attempt at a solution

Ok...here's how the teacher has solve this...

f(x)=(x-α)g(x)+B(remainder theorem)

g(x)=(x-β)∅(x)+A(remainder theorem)

f(x)=(x-α)[(x-β)∅(x)+A]+B

f(x)=(x-α)(x-β)∅(x)+A(x-α)+B

∅(x)[itex]\rightarrow[/itex]quotient

A(x-α)+B[itex]\rightarrow[/itex]remainder

But I think that he has forgotten to use the remainder theorem there..I can't see where he has applied it..

I think if we use the theorem,we have to do something like this.

f(x)=(x-α)g(x)+α

g(x)=(x-β)∅(x)+β

f(x)=(x-α)[(x-β)∅(x)+β]+σ

f(x)=(x-α)(x-β)∅(x)+β(x-α)+σ

Here we get something like A(x-α)+B as the remainder{β(x-α)+σ}..But I think that I'm wrong as its too easy then to determine A and B...like A=β and B=α...

Please someone show me were has he used the remainder theorem..Thanks !

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# Homework Help: Polynomial Remainder Therem to proove this

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