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Math: Basic Tutorials

Polynomials : sub-module 4 of 5 of math tutorials

Polynomials are expressions that are commonly encountered in algebra and have many practical applications in several different fields. This module will introduce you to what polynomials are and show you how to perform basic operations with polynomials, such as adding, subtracting, multiplying, dividing, and basic factoring.

 

Tips

  • Know your terminology. A polynomial is an algebraic expression made up of one or more terms, where a term is a constant or a product of a constant and one or more variables. A monomial has one term, a binomial has two terms, and a trinomial has three terms.
  • Identify the terms in a polynomial. Remember terms in a polynomial are separated by addition and subtraction and that like terms have the same variable raised to the same exponent.
  • To add and subtract polynomials, combine like terms. When adding and subtracting polynomials, first identify the like terms in the expression, and then add or subtract the numerical coefficients to simplify. You may find it useful to circle or underline like terms.
  • To multiply polynomials, use the distributive property and product property of exponents. When multiplying polynomials, multiply each term in the first expression by each term in the second expression. To multiply terms, multiply the numerical coefficients and add the exponents of the variables.
  • To divide monomials, use the equivalent fractions property and the quotient property of exponents. When dividing monomials, write the coefficients and each variable as separate fractions, and then reduce the coefficients and subtract the exponents of the variables to simplify.
  • The first step to factor polynomials is to factor out Greatest Common Factor (GCF). The GCF is the largest expression that will fit into each term in the expression.
  • Pay close attention to the signs of each term when doing basic operations with polynomials. It is easy to make mistakes with signs, especially when subtracting. Remember that with multiplication and division, if the signs are the same, the answer will be positive and if the signs are opposite, the answer will be negative.