Polynomials

Know the Where About

Welcome to this introductory chapter on Polynomials.

Before going any further let’s have a look at all that is there to be learnt here. In this section you will learn about its definition, parts and components and the rules that govern the legality.

Definition

It may be defined as the sum of products of coefficients and variables raised to whole number powers.

Did that sound confusing? No Worries, the example below is just what you need right now.

5x^2 + 4x + 7

That’s one for you.

In the above example there are a number of terms that have been added up. The terms in the above expression are

• 5x^2
• 4x
• 7

Let’s take the first term and dissect it.

In 5x^2 you will find two components.

One of them is 5. This is what is called coefficient. This is the constant part of a term. This is always a well defined number that has constant value that does not change.

The other component is x^2. This is the variable part of the term. x is the variable that can take up certain defined range of values. 2 is the exponent or the power that the variable is raised to. Now this power can be any whole number viz 3, 4, 5, 6 etc.

What are Legal Acceptables Names?

Does that sound weird? Well it just refers to the acceptable and unacceptable forms. Here I will share with you some insights on what a correct name is all about and more importantly what it is not about.

Take care of the following aspects when deciding if certain expresssions are correctly written or not.

• The variable cannot be raised to the power of negative integers.
• The variable cannot be raised to the power of a fraction.
• The variable cannot be raised to the power of a root.
• The variable cannot be raised to the power of an irrational number.

If any expression does not meet any one of the above criteria it cannot be called as polynomials.


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