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:
- 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.
- Variable: A alphabet used to donate a number. For example, 8x + 7 = 5 where x is variable assign to number 8.
- 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.
- Operator: Symbols used to perform different operations say addition (+), subtraction (-), multiplication (*),etc.
- Constants: These are the terms in the algebraic expression that contain only numbers. For example, 8x + 7 = 5 where 7 and 5 are constants.
- 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
- Polynomial is used in economics to represent cost functions which are used to interpret and forecast market trends.
- Polynomial is also used in meteorology to create mathematics models to represent weather patterns.
- Roller coaster designer uses the polynomial to describe the curves in their rides.
- Polynomial is used in construction or material planning.
- 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:
- Variables cannot have the negative or fractional exponent. ()
- Variable in the denominator. ()
- Variables inside a radical. ()
Example: Evaluate the following as polynomial or not
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.
Evaluate the following as polynomial or not. Give reason.