Chapter 8, Problem 8GYR

(a)

To determine

How to write the term $f\left(x\right)/g\left(x\right)$ as a sum of partial fractions if the function $g\left(x\right)$ is a product of distinct linear factors, when the degree of a polynomial $f\left(x\right)$ is less than the degree of a polynomial $g\left(x\right)$.

(b)

To determine

How to write the term $f\left(x\right)/g\left(x\right)$ as a sum of partial fractions if the function $g\left(x\right)$ consists of a repeated linear factor, when the degree of a polynomial $f\left(x\right)$ is less than the degree of a polynomial $g\left(x\right)$.

(c)

To determine

How to write the term $f\left(x\right)/g\left(x\right)$ as a sum of partial fractions if the function $g\left(x\right)$ contains an irreducible quadratic factor, when the degree of a polynomial $f\left(x\right)$ is less than the degree of a polynomial $g\left(x\right)$.

What needs to be done for the cases that involve the degree of a polynomial $f\left(x\right)$ being not less than the degree of a polynomial $g\left(x\right)$.