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Welcome to our Math lesson on The Definition of Monomials, this is the first lesson of our suite of math lessons covering the topic of The Definition of Monomials and Polynomials, you can find links to the other lessons within this tutorial and access additional Math learning resources below this lesson.
In Chapter 6, we briefly mentioned the concept of monomers and polynomials. Thus, a monomial is an algebraic expression consisting of the product of a real number called a coefficient and one or more letters representing variables, which are raised to certain natural powers. For example,
are all monomials, as all variables are preceded by a number (coefficient), and moreover, the variables are raised to positive integer powers.
On the other hand,
are not monomials, as their variables are not always positive integers. Indeed, from the properties of indices and roots (more specifically, 1/xn = x - n and √x = x1/2), we can write the above expressions as
Since the index of x in the second expression and that of y in the first and third expressions are not positive integers (y has a negative integer index, while x has a rational index), they are not monomials.
Which of the following algebraic expressions is a monomial?
|Tutorial ID||Math Tutorial Title||Tutorial||Video|
|11.1||The Definition of Monomials and Polynomials|
|Lesson ID||Math Lesson Title||Lesson||Video|
|11.1.1||The Definition of Monomials|
|11.1.2||The Definition of Polynomials|
|11.1.3||The Degree of Polynomials|
|11.1.4||The Names of Polynomials by Degree|
|11.1.5||Finding the Value of Polynomials|
|11.1.6||Finding the Zeroes of a Polynomial|
|11.1.7||Finding the Zeroes of Polynomials through Iterative Methods|
|11.1.8||The Homogenous and Non-Homogenous Polynomials|
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