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, 8*x*, 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: 3*x*, -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:

2*x* + 5, 6y-8 …

Quadratic polynomial:

A polynomial with degree as 2 is called quadratic *polynomial*.

Example:

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

Cubic polynomial:

A polynomial with degree as 3 is called cubic *polynomial*.

Example:

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

Bi quadratic polynomial:

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

Example:

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

So this is about **polynomial and types of polynomials.**

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