How Do You Divide a Polynomial by a Monomial Using Long Division?

How Do You Divide a Polynomial by a Monomial Using Long Division?

Note:

You can use long division to divide a polynomial by a binomial! Want to learn how? Check out this tutorial!

Keywords:

  • problem
  • example
  • long division
  • divide
  • polynomial division
  • divisor
  • dividend
  • remainder
  • polynomial divided by monomial

Background Tutorials

  • Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

      • What's a Dividend and What's a Divisor?What's a Dividend and What's a Divisor?

      What's a Dividend and What's a Divisor?

      When you do division problems, you need to know the vocabulary that people use to describe what number is being divided, and what number is doing the dividing. This tutorial will help you keep that vocabulary straight!

  • Fluently divide multi-digit numbers using the standard algorithm.

      • How Do You Do Long Division?How Do You Do Long Division?

      How Do You Do Long Division?

      We know that calculators are everywhere, but that doesn't mean that long division isn't important! Sometimes you won't be allowed to use a calculator, and when those times occur, you'll be thankful that you watched this video!

  • Identify parts of an expression using mathematical terms (sum, term, product, factor, quotient, coefficient); view one or more parts of an expression as a single entity.

      • What's a Coefficient?What's a Coefficient?

      What's a Coefficient?

      There is a bunch of vocabulary that you just need to know when it comes to algebra, and coefficient is one of the key words that you have to feel 100% comfortable with. Check out the tutorial and let us know if you want to learn more about coefficients!

  • Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

      • What are Like Terms?What are Like Terms?

      What are Like Terms?

      Combining like terms together is a key part of simplifying mathematical expressions, so check out this tutorial to see how you can easily pick out like terms from an expression

  • Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

      • How Do You Multiply Monomials?How Do You Multiply Monomials?

      How Do You Multiply Monomials?

      Multiplying monomials? Group constants and like variables together before you multiply. See how to find the product of three monomials in this tutorial.

      • What is a Polynomial?What is a Polynomial?

      What is a Polynomial?

      If you learn about algebra, then you'll see polynomials everywhere! In this tutorial, you'll learn the definition of a polynomial and see some of the common names for certain polynomials.

Further Exploration

  • Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + (r(x)/b(x)), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.