How do you divide algebraic expressions?

Division of Algebraic Expressions

A mathematical equation made up of variables and constant showing a certain relation between them is called an algebraic expression. Basic mathematical operations like addition, subtraction, multiplication, and division can be performed on algebraic expressions.

The division of algebraic expressions is also sometimes referred to as ‘Factorization of algebraic expressions. This is because the division of an algebraic expression produces its factors.

There are some rules for the division of algebraic expression which are given as follows:

Rule 1: If x is a variable and m, n are positive integers such that m>n then

Rule 2: Quotient of two monomials = (quotient of their numerical coefficients) × (quotient of their variables)

Rule 3: For dividing a polynomial by a monomial, divide each term of the polynomial by the monomial.

There are some separate rules in detail for dividing a polynomial by a polynomial

a. Arrange the terms of the dividend and divisor in descending order of their degrees.

b. Divide the first term of the dividend by the first term of the divisor to obtain the first term of the quotient.

c. Multiply all the terms of the divisor by the first term of the quotient and subtract the result from the dividend.

d. Consider the remainder (if any) as a new dividend and proceed as before.

e. Repeat the process till we obtain the remainder which is either 0 or a polynomial of degree less than that of the divisor.

Please remember that to avoid making any mistakes while doing the division of algebraic expressions, a person first should go through all the rules related to it. A person should also try to write all the steps while doing such a division process.