Introduction to Polynomials

The word “Polynomial” is originated from 2 word – “Poly” and “Nomial”. Poly means “many”, nominal refer to “terms”. The meaning of polynomial is associated expression that has several terms. It is defined as a single term or a sum of the finite number of the term. Polynomial can be operated for addition, subtraction, multiplication, and non-negative number exponents. Polynomials seem during a wide range of areas of arithmetic and science.

Polynomial consists of following:

1. Term: In Algebra a term is either a single number or variable or numbers and variables multiplied together. Terms are separated by + or − signs. For example, 8x + 7 = 5.
2. Variable: A alphabet used to donate a number. For example, 8x + 7 = 5 where x is variable assign to number 8.
3. Coefficient: A number used to multiply a variable. For example, 8x + 7 = 5 where 8 is a number used to multiply with the variable x.
4. Operator: Symbols used to perform different operations say addition (+), subtraction (-), multiplication (*),etc.
5. Constants: These are the terms in the algebraic expression that contain only numbers. For example, 8x + 7 = 5 where 7 and 5 are constants.
6. Exponent: An exponent refers to the number of times a number is multiplied by itself. For example, .

Polynomial standard form

General representation of polynomial: .

Where  is constant and we can do the following operations while solving polynomials: Addition of polynomials, Subtraction of polynomials and multiplication of polynomials.

x is the indeterminate. The word “indeterminate” means that it represents no particular value, although any value may be substituted for it and n are the positive numbers.

Application of Polynomials

1. Polynomial is used in economics to represent cost functions which are used to interpret and forecast market trends.
2. Polynomial is also used in meteorology to create mathematics models to represent weather patterns.
3. Roller coaster designer uses the polynomial to describe the curves in their rides.
4. Polynomial is used in construction or material planning.
5. Polynomial is used in electronics, chemistry, physics, etc.

Identification of Polynomials

Polynomial is a combination of terms separated using the operator. The following are not included in polynomial:

1. Variables cannot have the negative or fractional exponent. ()
2. Variable in the denominator. ()
3. Variables inside a radical. ()

Example: Evaluate the following as polynomial or not

1. 
2. 
3. 
4. 5
5. 

Solution: 1.  = This is not a polynomial because the variable has a negative exponent.

2. = This is a polynomial term.

3.  = Not a polynomial term because the variable is a radical.

4. 5 = This is a polynomial because one term is allowed.

5.  = Not a polynomial term because dividing by a variable is not allowed.

Exercise

Evaluate the following as polynomial or not. Give reason.

1. 
2. 
3. 
4. 
5. 
6. 8
7. 
8.