Polynomials are very very important to understand to be successful in algebra. As I promised in my previous articles, that we are going to explore algebra by taking two paths. Polynomials are the second path which goes to algebra destination as the first path, equations, we are pursuing already. The important note to remember is that the algebraic relations or algebraic expressions give rise to both the polynomials and equations. Also, the word phrases from the daily life give birth to algebraic relations.
I can say that the polynomials are a type of algebraic relations. Polynomials involve the whole number powers of variables. They don't have negative or fractional powers. In other words, it can be said that polynomials are the simplest form of the algebraic expressions.
A polynomial can have one to infinite number of terms. Also the polynomials can be classified according to the number of terms they contain. We will discuss the classification of the polynomials in my coming articles in more detail. The objective of this article is to introduce the grade eight or higher students with polynomials.
As the polynomials are the simplest form of the algebraic expressions, they are written without the use of equal sign. When an equal sign is included with a polynomial, then it is called a polynomial equation.
Following are some examples of polynomials;
1. 3c
2. 4x + 2y
3. 2m - n - 9
4. 8
5. 5a+ 3ab - 9
Notice, in example 4, number "8" is a polynomial which means all the numbers can be called as polynomials. These numbers have the variable with power zero.
In all other examples, the polynomials have variables with exponent one. But remember that, variables can have any whole number as their exponents (power). Don't be surprised by the polynomials having variables with powers such as, 3, 5, 7 or even higher.
If there is a variable at the bottom (at denominator) in an algebraic relation, that algebraic relation is not a polynomial. For example;
5xy - 3/x - 5
Notice that, 3 has x as its denominator, therefore above relation is not a polynomial. Keep in mind that, the variable at the denominator in a relation or one with a negative power are the same. If you see a negative power of a variable, decimal or fractional power of a variable in an algebraic relation, never ever consider that relation as a polynomial.
Polynomials are very important as they are used in calculus, in science, economics and in many other areas. So, stay tuned as more explanations about the polynomial and algebra are on their way.
