# Polynomial and types of polynomials

Learn what is a polynomial and types of polynomials. An algebraic expression which consists of variables and which has non-negative integral powers, then that algebraic expression is called a polynomial. In polynomial “poly” means many. So any algebraic expression which has variable power as non-negative integers. This means the power of polynomial maybe 0 or 1 or 2 or 3 and so on.

Basically, an algebraic expression with one or more terms is called polynomial. So if there is only one term then it is also a polynomial. Based on terms we have different names for polynomials that I will discuss in types of polynomials.

The below given are polynomials:

3${ x }^{ 2 }$ + 7y, 8x, 4${ y }^{ 6 }$ and 12${ x }^{ 4 }$-67${ y }^{ 9 }$.

All the above examples are with non-negative integral powers so they are called polynomials.

Note:

If there is only a constant then it is called constant polynomial. Remember that degree of any constant polynomial is always equals to  1.

The below given are not polynomials:

7${ x }^{ -5 }$ + 5y- this is not a polynomial as it contains negative power.

4$\sqrt { x }$ -3y – this is not a polynomial as the power is a fraction.

6y +  $\frac { 2 }{ x }$ this is also not a polynomial because the variable is in the denominator that means the power of x is negative.

## Types of Polynomials based on terms:

Monomial:

If a polynomial contains only one term then it is Monomial.

Example: 3x, -9${ y }^{ 2 }$

Binomial:

If a polynomial contains two terms then it is called binomial.

Example: 7y + 8z, 6${ a }^{ 4 }$ – 2y

Trinomial:

If a polynomial contains three terms then it is called trinomial.

Multinomial:

If a polynomial contains more than three contains then it is called multinomial.

### Types of polynomials based on degrees:

Linear polynomial:

A polynomial with degree as 1 is called linear polynomial.

Example:

2x + 5, 6y-8 …

A polynomial with degree as 2 is called quadratic polynomial.

Example:

4${ x }^{ 2 }$ + 7x, 9${ y }^{ 2 }$

Cubic polynomial:

A polynomial with degree as 3 is called cubic polynomial.

Example:

5${ y }^{ 3 }$-2x+7, 3${ a }^{ 3 }$+9x,…

6${ x }^{ 4 }$ -5x+2x, 4${ x }^{ 4 }$-7