Monday, 19 Apr 2021

How to divide polynomials: Complete Lesson

Division of polynomials might appear like the most difficult and challenging of the procedures to master. Still, so long as you can remember the basic guidelines about the long division of integers, it’s a surprisingly easy process. Let’s take a look at How to divide polynomials.

In this article, we are most likely to determine precisely how to solve the division between two monomials, a monomial and polynomial, and last but not least, between two polynomials.

Before diving into this concept of dividing polynomials, let’s briefly review a few essential terms here.

How to divide polynomials – Divide Polynomials by Long Division


It is an algebraic expression composed of two or even more deducted terms, included or increased. A polynomial can contain coefficients, variables, backers, constants and operators such as addition and reduction.

Additionally, crucial to keep in mind that a polynomial can not have fractional or adverse backers.

Examples of polynomials are; x3 + 2 x 2 − 9 x– 4, 3y2 + 2x + 5, 10 x 3 + 5 x + y, 4×2– 5x + 7) etc

There are three types of polynomials, particularly monomial, binomial and also trinomial.


It is an algebraic expression with only one term. Instances of monomials are; 5, 2x, 3a2, 4xy etc.


It is an expression containing two terms separated by either the addition sign (+) or reduction sign (-). Instances of binomial expressions are 2x + 3, 3x– 1, 2x +5 y, 6x − 3y etc.


A trinomial is an expression which contains exactly 3 terms. Instances of trinomials are: 4×2 + 9x + 7, 12pq + 4×2– 10, 3x + 5×2– 6×3 and so on

How to divide polynomials

The division is an arithmetic operation of splitting a quantity right into equal amounts. The division procedure is often described as repeated subtraction or reverses multiplication.

There are two techniques in mathematics for splitting polynomials.

These are the long division and also the artificial technique. As the name implies, the long division approach is an intimidating and challenging process to excel.

How to divide a monomial by an additional monomial?

When dividing a monomial by an additional monomial, we divide the coefficients and use the quotient legislation x m ÷ x n = x m– n to the variables.

NOTE: Any number or variable elevated to the power of no is 1. As an example, x0 = 1.

Let’s attempt a couple of examples below.


Divide 40×2 by 10x Option Separate the coefficients first 40/10 = 4 Currently separate the variables making use of the quotient guideline x2/ x = x2 -1= x.

Multiply the ratio of the coefficients by the rates of the variables.

⟹ 4 * x = 4x.


40×2/10x =

(2 * 2 * 5 * 2 * x * x)/ (2 * 5 * x).

Since x, two, and 5 are common elements of both the numerator, we cancel them bent on obtain.

⟹ 40×2/10x = 4x.

How to divide polynomials by monomials?

To separate a polynomial by a monomial, independently separate each polynomial term by the monomial. Later, add the quotient of each operation to get the response.

How to do a long polynomial division?

The lengthy division is the most ideal and reputable approach of separating polynomials; although the procedure is a little bit tiresome, the strategy is useful for all troubles.

The procedure of separating polynomials is just similar to splitting integers or numbers utilizing the lengthy division technique.

To separate two polynomials, here are the procedures.

Prepare both the divisor and dividend in coming down the order of their levels.

Separate the first regard to the dividend by the first regard to divisor to obtain the 1st regard to the quotient.

Determine the product of all the divisor’s terms and the 1st term quotient and deduct the reward’s answer.

If there is a remainder, continue as repeat treatment three until you get no as the remainder or receive an expression of a smaller sized degree.