Polynomials Explained With Examples

What is Polynomial?

The word polynomial is derived from the Greek words:

‘poly’ that means ‘many’

and ‘nominal’ means ‘terms’,

So, altogether it means“many terms”.

A polynomial can have any number of terms but not infinite.

Definition of Polynomials

Polynomials are the algebraic expressions that consist of variables and coefficients. We can perform all the arithmetic operations like addition, subtraction, multiplication and also taking positive integral power for polynomial expressions except division by variable.

Composition:
1.Constants:

E.g. 1, 2, 3 so on

2.Variables:

E.g. x, y, z etc.

Exponents:

E.g. x5, x9, x3 etc.

Notation

A polynomial in the variable “x” is the algebraic expression of the form

P(x) = anxn + an-1xn-1 + an-2xn-2 + …… + a1x + a. (an 0)

Here,

• “n” is the highest power of “x”.
• “an” is co-efficient of variables, a real number.
Further Reading:  Multiplicative Identity and Multiplicative Inverse
An example of Polynomials

P(x) = 6x3 + 4x2 + 2x + 5

n = 3, the highest power. and an = 6, 4, 2and 5 are the co-efficient of variables x3, x2, x1, x respectively.

Degree of a Polynomial

The degree of a polynomial is defined as the highest power of “x” in any polynomial.

Example:

In this Polynomial,

P(x) = 6x3 + 4x2 + 2x + 5

The highest power of variable i.e. x is 3. That’s why the degree of polynomial P(x) = 6x3 + 4x2 + 2x + 5

is 3.