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.

Polynomial and types of polynomials

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:

3x2 + 7y, 8x, 4y6 and 12x4-67y9.

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:

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

4√x -3y – this is not a polynomial as the power is a fraction.

6y +  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, -9y2

Binomial:

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

Example: 7y + 8z, 6a4 – 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.

Polynomial and types of polynomials

Types of polynomials based on degrees:

Linear polynomial:

A polynomial with degree as 1 is called linear polynomial.

Example:

2x + 5, 6y-8 …

Quadratic polynomial:

A polynomial with degree as 2 is called quadratic polynomial.

Example:

4x2 + 7x, 9y2

Cubic polynomial:

A polynomial with degree as 3 is called cubic polynomial.

Example:

5y3-2x+7, 3a3+9x,…

Bi quadratic polynomial:

A polynomial with degree as 4 is called bi quadratic polynomial.

Example:

6x4 -5x+2x, 4x4-7

So this is about polynomial and types of polynomials.

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