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High School Algebra - Real Numbers and Polynomials

This free online course on Alison takes you through the basics of algebra from real numbers, binomials, and polynomials.

Publisher: ADU
This free online course takes you through the definition and properties of real numbers. The course introduces the learners to the techniques used in performing basic operations with radicals as well as the differences between non-positive integral exponents and zero exponents. By the end of the course, the learner will be very much acquainted with operations using rational expressions as well as multiplying monomials and polynomials.
High School Algebra - Real Numbers and Polynomials
  • Duration

    5-6 Hours
  • Students

  • Accreditation






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Real numbers comprise different types of numbers, prominent among them are the rational numbers and the irrational numbers. This course explains the various properties of irrational numbers and how they are linked in the practice of algebra. Are you familiar with the number line system in mathematics? Did you know that all irrational numbers maintain a particular position on the Real number line? Get to learn about the uniqueness of rational and irrational numbers on a real number line. By taking this course, you will get full details on the set of numbers that make up Real numbers. The course will take you through the different evaluation methods for calculating the square root of a number. We have seen in elementary mathematics that finding the square root of a perfect square can be quite easy. But, when the radicand is not a perfect square, there are proven and tested methods that can be used to find the approximate value of the square root. The course will take you through the approaches employed by mathematicians in finding the square of perfect squares. 

Do you know that operations like addition, subtraction, multiplication and division can be performed with radicals? These operations are valid for square roots, cube roots, and even fourth roots. You will study the simplification of radicals, how to add and subtract radicals as well as the use of radicals in problem-solving. Simplifying radicals can be sometimes daunting! To simplify radicals, you must have a good knowledge and understanding of perfect squares, perfect cubes, or other roots, as well as the Product Property of square roots. You will learn how to add or subtract radicals by ensuring the index or root must be the same, and the radicands must also match. You will study equations containing a variable under the radical sign called a radical equation. There are instances where an algebraic expression contains only a singular term. An algebraic expression involving a singular term is called a monomial. A monomial can exist as a Real number in constant form or as a variable. It can also be expressly written as the product of a Real number and other variables. Monomials are a very interesting aspect of algebra. In working with monomials, we will need to learn the laws for exponents. 

Furthermore, you will get to study some extremely useful scientific notations relevant to algebra. Scientific notations are quite important when we deal with large numbers. They can also be called to action if we work with very small numbers. As a student, having the basic knowledge of scientific notation ensures you are able to write or compute with extreme numbers more easily. Another interesting concept you will get to learn about in this course is polynomials. A polynomial is an expression with two or more monomial terms combined by addition and/or subtraction. An interesting mathematical wonder is the formation of polynomials. Monomials combine to form a polynomial. Each monomial making up the polynomial is known as a term. Polynomials can be classified in different ways, including constant polynomial, linear polynomial and quadratic polynomial. You will be introduced to different operations that can be performed on a polynomial, including addition, subtraction as well as using Associative, Commutative and Distributive Properties. This course also elaborates on Binomials which are expressions consisting of two monomials combined by an addition or subtraction sign. Are you having difficulties with dividing polynomials? This course has got you covered! The course covers in detail the two methods for dividing polynomials - the long division method and the synthetic division method. Are you a student or graduate of mathematics looking to build your knowledge of algebraic operations? Then this course is a perfect fit for you.

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