Polynomials and Factorization for General Studies
Learn about the polynomial concepts, factorization methods and rational expressions in this free online course.Publisher: ADU
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This course is the third in a series of algebra in a mathematics courses. Polynomials and Factorization is a free online course that has been specially prepared to take you through an introductory level to working with Polynomials and Factorization. Learning about the applications of polynomials and factoring can be tough because polynomials and factorization is a vast topic. However, this course is designed to make the learning process easier. What are polynomials? How do you add and subtract polynomials? What are operations with rational expressions? In this course, each section helps you understand polynomials and factoring with the aid of examples. A polynomial is formed by combining two or more monomials using the operations of addition and/or subtraction. Each monomial making up the polynomial is known as a term. You will learn about the different types of polynomials, the terms, and their various definitions.
This course prepares you to learn about polynomials by taking you through mathematical operators with polynomials. The addition and subtraction of polynomials can be performed by using the Associative, Commutative and Distributive Properties. The like terms (monomials) can be combined using the indicated operation. The course is not only limited to the addition and subtraction of polynomials, it also discusses the multiplication and division of polynomials. In order to do this, you must learn about these properties and how they can be applied. This course illustrates how synthetic division works. Synthetic division is a quick condensed way of performing long division when a polynomial with a degree greater than or equal to 1 is divided by a binomial in the form of (x-c). The synthetic division also indicates if the binomial is a factor of the polynomial or if it is not. You will learn about the differences between using long division and synthetic division. This course explores how to solve fractional equations by finding the lowest common denominator for all the terms in the equation and multiplying both sides of the equation by the LCD.
Furthermore, you will learn about Factoring in Algebra. To factor a polynomial means that it is expressed as the product of other polynomials. Just like in arithmetic, where it is sometimes useful to represent a number in factored form in algebra, it can be useful to represent a polynomial in factored form. One way to do this is by finding the greatest common factor of all the terms. You will learn about how to find the greatest common factor of a polynomial or monomial. Other factoring methods like factoring the difference of two perfect squares, factoring the trinomials, factoring by grouping terms, and factoring completely are discussed in this course. The most fundamental tools for solving equations are addition, subtraction, multiplication, and division. These methods work well for equations like x + 2 = 10 - 2x and 2(x - 4) = 0. But what about equations where the variable carries an exponent, like x2 + 3x = 8x - 6? This is where solving equations with factoring comes in. You will learn how to solve equations by factoring and the problem-solving application of factoring. So, register for this course and start your next learning journey.
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Introduction to Polynomials
Introduction to Polynomials - Learning Outcomes
Definitions and Vocabulary
Multiplication of Polynomial
Division of Polynomial
Introduction to Polynomials - Lesson Summary
Introduction to Polynomials - Assessment
Introduction to Factorization
Introduction to Factorization - Learning Outcomes
Perfect Square Trinomials
Introduction to Factorization - Lesson Summary
Introduction to Factorization - Assessment
Upon the successful completion of this course, you should be able to:
- Identify the characteristics of a polynomial.
- Explain how to divide monomials and polynomials.
- Analyze operations with rational expressions.
- Identify how to solve fractional equations.
- Explain the different types of polynomials.
- Analyze factoring the difference of two perfect squares.
- Explain the sum and difference of two perfect cubes.
- Describe how to multiply monomials and polynomials.
- Identify how to solve equations by factoring.
- Explain how simplify rational expressions.
- List some of the problem-solving applications of factoring.
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