In this set of Math Tutorials we cover Polynomials in details with clear guides, Polynomials formulas and working examples. Each tutorial includes example questions, a revision guide and supporting Polynomials calculators
We also provide online Polynomials Calculators which allow you to calculate specific Polynomials formula in support of the tutorials or to check and verify your own calculations in support of your Polynomials homework, math coursework or to help you improve your own understanding so it is easier to teach your children Polynomials.
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This chapter is about polynomials - a fundamental concept in algebra you will encounter in many situations when dealing with math. The first tutorial begins with monomials as the building block of polynomials where their structure and components are explained. Then, the tutorial continues with polynomials (combinations of two or more monomials), where the difference between polynomials and algebraic expressions is highlighted to avoid confusion when explaining concepts in future tutorials and lessons. Other concepts such as the degree of a polynomial, the terms, coefficients and constant of a polynomial, the value and zeroes of a polynomial, homogenous and non-homogenous polynomials etc., are among the math concepts discussed in this tutorial. Perhaps the most challenging task when dealing with polynomials consists of finding the zeroes of high-order polynomials - which is explained at the end of the first tutorial.
The second tutorial deals with operations with polynomials. It begins with the difference between like and unlike terms, and then it follows with the meaning of the leading term and leading coefficient of a polynomial. Another thing you should understand before starting with operations with polynomials is how to write a polynomial in the standard form. The tutorial then continues with operations with polynomials (addition, subtraction, multiplication and division), and in particular, the division of a polynomial with a monomial and how to divide two polynomials. Other things explained in this tutorial include raising a polynomial to a given power, graphing a polynomial, as well as finding the zeroes of a polynomial analytically and from its graph.
The third tutorial of this chapter is a continuation of the second tutorial that focuses on the division of polynomials. It begins with the method of synthetic division of polynomials; then it continues with the components of the division of two polynomials and the procedure used in the division of polynomials when using the Synthetic Division Method. Again, in this tutorial, the roots of a polynomial are discussed, where you will see that the Rational Root (Zero) Theorem is very helpful in finding the roots and solving polynomial equations. Other questions that are answered in this tutorial include: how to list all possible roots (zeroes) of a polynomial equation; how to identify the zeroes of a polynomial from the whole list of possible zeroes; and how to solve polynomial equations in general.
The fourth (and last) tutorial of this chapter deals with rational expressions. They are expressions formed when one polynomial divides another polynomial. The first part of the tutorial deals with general concepts like the definition of rational expressions; the meaning of relatively prime factors, and so on. Then, the tutorial continues with the methods used to convert an algebraic fraction into a rational expression; the meaning of the disallowed values in a rational expression and how to find them; how to simplify the rational expressions. The tutorial continues with basic operations with rational expressions. An important thing you will learn in this tutorial is the calculation of the Least Common Multiple (LCM) of two or more monomials. The tutorial concludes with complex fractions - both recurring and constant - where you will learn how to calculate their value in various situations.
The following Math Calculators are provided in support of the Polynomials tutorials.