Partial Fraction Decomposition

Vocabulary

degree of a polynomial

degree of the term in a polynomial with the greatest degree

degree of a term

exponent of the variable of a term in a polynomial in one variable

improper fraction

rational expression where the degree of the numerator is greater than or equal to the degree of the denominator

irreducible

expression that cannot be written in a simpler form as a product of factors

linear factor

factor of a polynomial in the form $(x + n)$, where $n$ is a constant

partial fraction

for the rational expression $\frac{P}{Q}$, a rational expression with a denominator that has a degree less than the degree of $Q$, such that the sum of the partial fractions is equal to $\frac{P}{Q}$

partial fraction decomposition

process of writing a rational expression as a sum of partial fractions, which are rational expressions with a denominator of lower degree

proper fraction

rational expression where the degree of the denominator is greater than the degree of the numerator

rational expression

expression in the form $\frac{P}{Q}$, where $P$ and $Q$ are polynomials and the value of $Q$ is not zero