3 fully explained Inverse Laplace Transform Example Problems including Partial Fraction Decomposition, sometimes called Partial Fraction Expansion. In this Partial Fraction Decomposition example problem, you'll also learn how to factor a polynomial, and what to do about repeated roots, also called repeated factors. Last step to solve these 2nd order Linear ODEs is to use Laplace Transform Tables to perform an Inverse Laplace Transform to return to the time domain from the frequency domain to find the general solution. CHAPTERS 0:00 Partial Fraction Decomposition 4:53 How to Factor a Polynomial 9:42 Partial Fractions Repeated Factors