How Do You Divide a Rational Expression by a Polynomial?

How Do You Divide a Rational Expression by a Polynomial?

Note:

Dividing a rational expression by a polynomial is easier than you might think! Follow along as this tutorial takes you through that process step-by-step!

Keywords:

  • problem
  • rational
  • rational expression
  • divide
  • polynomial
  • factor
  • factor polynomials
  • cancel
  • factoring
  • common factors
  • reciprocal
  • division
  • divide rational expressions
  • difference of squares
  • simplify
  • algebraic fraction
  • variable
  • multiply
  • multiply rational expressions
  • divide fractions

Background Tutorials

  • Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.

      • What's a Reciprocal?What's a Reciprocal?

      What's a Reciprocal?

      Reciprocals are important when it comes to dividing fractions, finding perpendicular lines, dealing with inverse proportions, and so much more! In this tutorial you can review the basics about reciprocals.

  • Use the structure of an expression to identify ways to rewrite it.

      • How Do You Know if You Have a Difference of Squares?How Do You Know if You Have a Difference of Squares?

      How Do You Know if You Have a Difference of Squares?

      Not sure if the binomial you've factoring is a difference of squares problem? This tutorial will show you what characteristics the binomial must have in order to be a difference of squares problem. Take a look!

  • Factor a quadratic expression to reveal the zeros of the function it defines.

      • How Do You Factor a Trinomial?How Do You Factor a Trinomial?

      How Do You Factor a Trinomial?

      Factoring trinomials can by tricky, but this tutorial can help! Follow along as a trinomial is factored right before your eyes! Then, check your answer by using the FOIL method to multiply the binomials back together and see if you get the original trinomial.

  • 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.

      • 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.

  • Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

      • How Do You Reduce Common Factors in a Rational Expression?How Do You Reduce Common Factors in a Rational Expression?

      How Do You Reduce Common Factors in a Rational Expression?

      Multiplying rational expressions? Want to cancel common factors out to make things easier to work with? In this tutorial, you'll see how to cancel out common factors in order to find the simplified product of two rational expression. Check it out!

      • How Do You Multiply Quotients of Monomials?How Do You Multiply Quotients of Monomials?

      How Do You Multiply Quotients of Monomials?

      Multiplying together two monomials isn't so hard, especially if you know the proper steps! This tutorial will take you through all the steps necessary to multiply together two monomials. Then, you'll see how to divide the numerator and denominator by the greatest common factor (GCF) in order to simplify and get your answer!

Further Exploration

  • Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

      • How Do You Multiply a Rational Expression by a Polynomial?How Do You Multiply a Rational Expression by a Polynomial?

      How Do You Multiply a Rational Expression by a Polynomial?

      To multiply a rational expression by a polynomial, just turn that polynomial into a fraction, multiply, and simplify to get your answer! This tutorial shows you that process step-by-step!

      • How Do You Multiply Two Rational Expressions?How Do You Multiply Two Rational Expressions?

      How Do You Multiply Two Rational Expressions?

      Multiplying together two rational expression isn't so hard, especially if you know the proper steps! This tutorial will take you through all the steps necessary to multiply together two rational expressions and then simplify the product to get the answer. Check it out!

      • How Do You Divide Two Rational Expressions?How Do You Divide Two Rational Expressions?

      How Do You Divide Two Rational Expressions?

      Dividing two rational expressions? Turn it into a multiplication problem by multiplying by the reciprocal of the second rational expression (the divisor)! This tutorial shows you how to do just that! Then, you'll see how to perform the multiplication and simplify to get you answer!