Math Is Fun Forum

yonski

Member

Registered: 2005-12-14

Posts: 67

Remainder Theorem

Hi there,
how would i go about expressing the following improper fraction in 'mixed' number form, using the remainder theorem?...

(2x^2 + 4x + 5) / (X^2 - 1)

Would it be correct to write it as:

A(x^2 - 1) + (Bx + C)/(x^2 - 1)

And then find the values of A, B and C? I know it's something like that.

Thanks for any help!
Jon.

Last edited by yonski (2007-02-19 09:14:20)

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Student: "What's a corollary?"
Lecturer: "What's a corollary? It's like when a theorem has a child. And names it corollary."

fredekr

Member

Registered: 2007-02-20

Posts: 5

Re: Remainder Theorem

Would it be correct to write it as:

A(x^2 - 1) + (Bx + C)/(x^2 - 1)

And then find the values of A, B and C? I know it's something like that.

Thanks for any help!
Jon.

No, that's not right. The Remainder Theorem tells you about roots and remainders. It looks to me like you're trying to divide polynomials (the first step in the applying the Remainder Theorem). For this problem, "long division" is the answer.

Try looking at this page:
http://www.purplemath.com/modules/polydiv3.htm
(look at the 2nd, 3rd, and 4th examples)

If that makes sense to you, great!

(If it doesn't it may be because you were taught a different division method in primary school -- US students are taught this method for basic division, but most European student are taught other techniques. If it doesn't makes sense, try searching on "long division" and do some simple problems with real numbers until you get the hang of the long division method when there's a remainder. Then go back to the polynomial division.)

cheers,
Kevin

Last edited by fredekr (2007-02-20 18:12:39)