The division operation is one of the fundamental mathematical operations used for solving arithmetic problems. Long division is a traditional procedure used for dividing two numbers, where the divisor has several digits. The process can be time-consuming, and alternative methods can be used to solve such arithmetic problems. Synonyms for long division include polynomial division, partial quotients division, and synthetic division. Polynomial division is a method of dividing two polynomials, while partial quotients division is a method of breaking down the dividend into smaller parts. Synthetic division is a shorthand method used for dividing polynomials using only their coefficients. Each of these methods has its unique advantages and can be used based on the nature of the problem.