Laws of Exponents and Factoring in Algebra
Learn about the concept of non-positive exponents in algebra and how to factor polynomials from this free online course.Publisher: ADU
CertificationView course modules
This free online course on the laws of exponents and factoring in algebra will begin by introducing you to the concept of monomial as an algebraic expression in mathematics. You will learn about the relationship between variable and exponent appearing, along with the multiplication, addition, and division of monomials. You will also learn about the components of a monomial. This course will delve into what makes the exponents of monomial negative integer or zero. You will then learn how to simplify the non-positive monomial exponents and what scientific notation is used for in algebra. This course will then teach you about the various ways to solve fractional equations. You will also learn how an expression with two or more monomial terms are combined by addition, subtraction, and division. Get to understand the use of associative and commutative properties in solving monomial equations along with the laws for dividing monomials in mathematics.
Do you know how to find the lowest common denominator (LCD) when solving algebraic equations? This course will explain in detail how to multiply both sides of an equation with the lowest common denominator. Get to understand the functions of the greatest common factor (GCF) as the first step of factoring polynomial equations. This course will further explain how to reverse distributive properties in factoring polynomials as well as how to get the difference of two perfect squares using the FOIL method. You will then learn about the combination of factors that can be added together to get the coefficient of the middle term of a polynomial. This course will also teach you how exponents are arranged in descending order in polynomial equations. You will then learn how to factor the sum of two perfect cubes as well as the difference between two perfect cubes in the real number system.
Finally, the course will expose you to the formula for factoring the sum of two perfect cubes and what it means to factor a polynomial completely. You will be introduced to the procedures involved in factoring a polynomial completely. Get to learn about the different approaches to the multiplication of polynomials. This course is designed to teach you about the associative properties, commutative properties, and distributive properties of multiplying polynomials. Upon the successful completion of this course, you will be equipped with the requisite knowledge about the laws guiding the multiplication of monomials and polynomials in algebra. You will also be able to differentiate between the composition of a monomial and a polynomial. This course is targeted at teachers, students, facilitators, engineers, mathematicians, as well as anyone enthusiastic about solving algebraic equations. Start this course today to expand your knowledge on the laws of exponents as well as factoring monomials and polynomial expressions.Start Course Now
Monomials and Laws for Exponents
Monomials and Laws for Exponents - Learning Outcomes
Definitions and Vocabulary
Polynomials - Multiplication and Division
Multiplication of Polynomials
Division of Polynomials
Solving Fractional Equations
Monomials and Laws for Exponents - Lesson Summary
Factoring Methods - Learning Outcomes
Greatest Common Factor
Trinomials in Factoring
Sum and Difference of Two Perfect Cubes
Problem Solving Applications
Factoring Methods - Lesson Summary
Upon the successful completion of this course, you will be able to:
- Identify the vocabulary associated with monomials.
- Discuss the addition and subtraction process of monomial.
- Explain what the power of a power means as it relates to monomials.
- Analyze the various methods of factoring a monomial.
- Explain how to find the greatest common factor (GCF).
- Discuss how to factor the difference of two perfect squares.
- Recall how factoring of trinomial works.
- Explain factoring by grouping.
- Illustrate factoring completely with mathematical equations.
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