Polynomials and Factorization for General Studies

This course is the third in a series of algebra Mathematics courses and has been specially prepared to take you through the fundamentals of working with polynomials and factorisation. Learning about the applications of polynomials and factoring can be challenging because it is such a vast topic. However, we have designed this course to make the learning process easier. What are polynomials and how do you add and subtract them? What are operations with rational expressions? In this course, each section will help you understand polynomials and factoring with the aid of examples. You form a polynomial 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 polynomials, the terms and various definitions.

We then prepare you further by taking you step by step through mathematical operators with polynomials. You can add and subtract polynomials using the associative, commutative and distributive properties. The ‘like’ terms (monomials) can be combined using the indicated operation. We then discuss the multiplication and division of polynomials. To do this, you must learn about their properties and how they can be applied. We illustrate 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 not. We demonstrate the differences between using long division and synthetic division. We explore how to solve fractional equations by finding the lowest common denominator (LCD) for all the terms and multiplying both sides of the equation by the LCD.

This course moves on to factoring in algebra. To ‘factor’ a polynomial means that you express it as the product of other polynomials. Like in arithmetic, 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 discover how to find the greatest common factor of a polynomial or monomial. We investigate other factoring methods like factoring the difference of two perfect squares, factoring the trinomials, factoring by grouping terms and factoring completely. The 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. So register for this course and learn to solve equations by factoring and the problem-solving application of factoring.