Partial fraction decomposition involves representing a fraction consisting of polynomials as a sum of a quotient polynomial, and another fraction. This technique is useful in integration.
Definition
Let and be two polynomials, where the degree of is greater than that of . Then we can use polynomial long division to obtain:
- is the quotient polynomial
- is the remainder polynomial. The degree of is always less than .
The remainder polynomial can then further be decomposed into partial fractions, based on the form of :
Denominator Form () | Also called | Decomposition |
---|---|---|
Linear Factors | ||
Repeated Linear Factor | ||
Repeated Linear Factor | ||
Irreducible Quadratic Factor | ||
Irreducible Nth Factor | ||
![[ape_rational_pf.gif | ape_rational_pf.gif]] |