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# Polynomials: Types and Examples

## What is a Polynomial?

An expression of the form p(x) = a+ a1x + a2x2 +….+anxn, where  an ≠ 0 is called a  polynomial in x of degree n.

Here a0, a1, a2,….., an  are real numbers and each power ox x is a non-negative integer. A polynomial can be

• constants (like 5, −10, or ½)
• variables (like x and y)
• exponents (like the 3 in x3 ), but only 0, 1, 2, 3, … etc are allowed

### Examples:

(i)  3x + 5 is a polynomial in x of degree 1.

(ii) 4y2 -3y +8 is a polynomial in x of degree 2.

(iii) 2u3 + 4u2 -5u + √3 is a polynomial in u of degree 3.

(iv)√(x+3), 1/(x+2), etc, are not polynomials

## Polynomial or Not?

These are polynomials:

• 5x
• x − 4
• −4y2 − (79)x
• 4xyz + 3xy2z − 0.1xz − 200y + 0.5
• 512v5 + 99w5
• 9

(Yes, “9” is a polynomial because it can be just a constant!)

These are not polynomials

• 5xy-4 is not polynomials, because the exponent is “-4” (exponents can only be allowed 0,1,2,…)
• 2/(x+4) is not, because dividing by a variable is not allowed
• 1/x is not either
• √x is not, because the exponent is “½”.

## Degree of a Polynomial

The degree of a polynomial is defined as the largest degree of a monomial within a polynomial. Thus, a polynomial equation having one variable which has the highest exponent is called a degree of the polynomial.

Polynomial Degree Example
Constant or Zero Polynomial 0 10
Linear Polynomial 1 5x+3
Cubic Polynomial 3 2u3-3u3+8u+1
Quartic Polynomial 4 2y4+3y3-5y2+9y+1

Example: Find the degree of the polynomial 4u4 – 5u3+ 6u2 -8u+3

Solution:

The degree of the polynomial is 4.

## Types of Polynomials

Polynomials are of three separate types and are classified based on the number of terms in it. The three types of polynomials are given below:

1. Monomial
2. Binomial
3. Trinomial

These polynomials can be together using addition, subtraction, multiplication, and division but is never division by a variable. A few examples of Non Polynomials are: 1/x+4, x-5