How Do You Divide Two Polynomials by Factoring and Canceling?

How Do You Divide Two Polynomials by Factoring and Canceling?

Note:

Simplifying a rational expression? You could factor the numerator and denominator and then cancel like factors. Learn what to do in this tutorial!

Keywords:

  • problem
  • rational
  • rational expression
  • variable
  • variables
  • fraction
  • algebraic fraction
  • fractions
  • numerator
  • denominator
  • simplify
  • cancel
  • common factor
  • factor
  • factor polynomials
  • divide
  • polynomial

Background Tutorials

  • Interpret parts of an expression, such as terms, factors, and coefficients.

      • What is a Constant?What is a Constant?

      What is a Constant?

      Constants are parts of algebraic expressions that don't change. Check out this tutorial to see exactly what a constant looks like and why it doesn't change.

  • 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.

      • How Do You Factor a Polynomial by Guessing and Checking?How Do You Factor a Polynomial by Guessing and Checking?

      How Do You Factor a Polynomial by Guessing and Checking?

      Factoring trinomials can by tricky, but this tutorial can help! Follow along as a trinomial is factored using the guess and check method. What, no possibilities work? The trinomial must be prime! Watch this tutorial and see what happens!

  • 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's FOIL?What's FOIL?

      What's FOIL?

      The FOIL method. No, not aluminum foil! The FOIL method stands for First, Outer, Inner, and Last. It's a popular way multiply two binomials together. This tutorial makes the FOIL method a breeze!

  • 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.

      • What's a Rational Expression?What's a Rational Expression?

      What's a Rational Expression?

      Got a fraction with a polynomial in the numerator and denominator? You have a rational expression! Learn about rational expressions in this tutorial.

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.

  • 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 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!