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Multiplication and Division of Polynomials

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More Lessons for Intermediate Algebra
More Lessons for Algebra
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A series of free, online Intermediate Algebra Lessons or Algebra II lessons.
Videos, worksheets, and activities to help Algebra students.

In this lesson, we will

  • review multiplying polynomials
  • learn how to multiply complicated polynomials
  • learn how to divide polynomials using long division

Review Multiplying Polynomials

There are different methods for multiplying polynomials. One method is to use an area model, but another way to multiply polynomials without having to draw diagrams, is to multiply polynomials using distribution. In order to understand multiplying polynomials, we need knowledge of multiplying monomials and binomials and to know the rules of multiplying exponents.

Multiplying Monomials and/or Binomials and FOIL
Multiplying Polynomials using Area Models 
Multiplying Larger Degree Polynomials using Distributing 
Multiplying Polynomials: Special Cases 

Multiplying Complicated Polynomials

When multiplying polynomials, sometimes we come across complicated polynomials that we can use substitution and multiplication to solve. When we have a trinomial where a binomial follows the (a-b)(a+b) format, simply substitute the entire binomial in for one of the variables and simplify.

How to multiply ugly polynomials by looking for patterns? Multiplying Polynomials - Slightly Harder Examples #1 Multiplying Polynomials - Slightly Harder Examples #2

Dividing Polynomials using Long Division

When dividing polynomials, we can use either long division or synthetic division to arrive at an answer. Using long division, dividing polynomials is easy. We simply write the fraction in long division form by putting the divisor outside of the bracket and the divided inside the bracket. After the polynomial division is set up, we follow the same process as long division with numbers.

Review Dividing a Polynomial by a Monomial

Polynomial Division: Long Division, Dividing by a binomial Examples of how to divide a degree two trinomial by a degree one binomial Example of how to perform long division by dividing a degree three polynomial by a degree one binomial.
There are no missing terms in the dividend. The quotient has a remainder. How to perform long division by dividing a degree three polynomial by a degree one binomial?
There are missing terms in the dividend. The quotient has fractional coefficients and there is a remainder. How to perform long division by dividing a degree three polynomial by a degree two binomial?
The quotient has a remainder.

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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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