How to Divide Polynomials By Monomials

••• Zolga_F/iStock/GettyImages

Once you've learned the basics of polynomials, the logical next step is learning how to manipulate them, just as you manipulated constants when you first learned arithmetic. Dividing polynomials might seem like the most intimidating of the operations to master, but as long as you remember the basic rules about adding and subtracting fractions and simplifying them, it's a surprisingly simple process.

TL;DR (Too Long; Didn't Read)

Write the division out as a fraction, with the polynomial as the numerator and the monomial as the denominator. Then break the polynomial apart into individual terms (each over the denominator/divisor) and simplify each term.

Dividing a Polynomial by a Monomial

Consider the following example: Divide the polynomial 4x3 – 6_x_2 + 3_x_ – 9 by the monomial 6_x_ using the following steps:

    Write the division out as a fraction, with the polynomial as the numerator and the monomial as the denominator:

    (4x3 – 6_x_2 + 3_x_ – 9)/6_x_

    Rewrite the fraction as a series of individual terms, each over the denominator:

    (4_x_3/6_x_) – (6_x_2/6_x_) + (3_x_/6_x_) – (9/6_x_)

    Simplify each of the terms as much as possible. Continuing the example, this gives you:

    (2_x_2/3) – (x) + (1/2) – (3/2_x_)


    • You can check your work by multiplying the result by the original divisor. Concluding this example, you'd have:

      [(2_x_2/3) – (x) + (1/2) – (3/2_x_)] × 6_x_ = 4x3 – 6_x_2 + 3_x_ – 9

      Because multiplying gives you the same polynomial you started with, your answer is correct.

Related Articles

How to Divide Rational Numbers
How to Divide in Scientific Exponents
How to Factorise a Quadratic Expression
How to Simplify Exponents
How to Calculate the Area of a Curved Surface
How to Factor Polynomials With 4 Terms
How to Write a Rational Number as the Quotient of Two...
How to Factor Polynomials Step-by-Step
How to Factor Binomial Cubes
How to Do Fractions With a TI 83 Calculator
How to Find the X Intercept of a Function
Algebra 1 Compared to Algebra 2
How to Convert a Fraction to a Ratio
How to Convert Pounds Per Square Foot to PSI
How to Convert PPH to GPM
How to Divide Fractions With Different Denominators
How to Find Equations of Tangent Lines
How to Calculate Volume of a Rectangular Prism
How to Solve Distributive Properties With Fractions
How to Find the Inverse of a Given Number