CALCULUS Understanding Its Concepts and Methods

Partial fractions, Irreducible polynomial

In the method of partial fractions, we write
an arbitrary rational function as a polynomial plus a sum of rational
functions of the
formand
of the
formwhere
*a *≠ 0
and
*b*^{2} -
4*ac* < 0
. For example,

A polynomial
*ax*^{2} + *bx* + *c*
with
*b*^{2} -
4*ac* < 0
has no real roots, so it cannot be factored as the product of polynomials of
smaller degree. Such a polynomial is called
irreducible.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.