## How to Do Operations with Polynomials

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### How can we Define Polynomials?

To understand the proper definition of polynomials, we must break the word into two “**poly**” and “**nomials**”. This means a variety of expressions. To be extremely precise, a polynomial is an algebraic expression which contains various terms **separated **by certain mathematical operations. These terms can be pure variables, pure constants, or even mixed terms such as variables with **coefficients**. Now, a crucial point to determining a polynomial is that the variable in the expression (suppose \(x\)), should **not **have a **fractional **power.

For example, \(2x^{\frac{1}{3}} \ + \ 3x \ + \ 1\) is **not **a polynomial as the first term has a **fraction power **of \(x\).

### Types of Polynomials

Based on the number of terms, there are 3 different types of polynomials. They are monomials, binomials and trinomials. Let’s discuss more about them:

**Monomial**: They consist of just a**single**term but there is one condition. The term**cannot**be zero. Ex: \(6x^2, \ 7x^3, 67x\), etc.**Binomial**: Binomials consist of just**two**terms and they must have a mathematical operation in between. Ex: \(6x^2 \ + \ 7x^3, \ 8x^2 \ + \ 7y, \ xy^2 \ + \ 3x\), etc.**Trinomial**: Trinomial consist of**three**terms and between every two terms there is a mathematical operation. Ex: \(2x^2 \ + \ 3x \ + \ 10, \ 4x^3 \ + \ 3x^2 \ + \ 7, \ 3x^2y \ + \ 4xy \ + \ 6\), etc.

### What are Like and Unlike Terms?

In algebra, we have the concept of like and unlike terms. So, if in an expression, you find that two or more same **variables **have the **same **exponential **powers**, then they are considered **like terms**. So, what we can do to simplify the expression is club those like terms by performing basic mathematical operations between them.

Also, in the case of **unlike **terms, you will find that the exponential powers of two or more same variables are **not **the **same**. So, we have no other option other than to leave them as they are.

Some **examples **of **like **terms are \(2x^3 \ - \ x^3, \ 7x^2 \ + \ 3x^2\). Here we can see that the power of \(x\) is the same in both the examples. Also, some examples of **unlike **term expressions would be \(7x^2 \ - \ 9x^3, \ -x^3 \ + \ x^2\).

### Operations with Polynomials

When operating with polynomial expression, apply the below-mentioned steps:

- First,
**simplify**the expression by adding/subtracting the like terms. Also. Don’t forget to apply the**PEMDAS**rule in case of brackets or parenthesis. - Also, wherever possible, use the
**distributive**property.

**Ex: **\(4x^3 \ + \ 3x^3 \ + \ 2x^2 \ - \ x^2 \ + \ 9 \ = \ 7x^3 \ + \ x^2 \ + \ 9\).

## Operations with Polynomials Practice Quiz

### More Polynomials courses

- How to Classify Polynomials
- How to Write Polynomials in Standard Form
- How to Multiply Monomials
- How to Simplify Polynomials
- How to Add and Subtract Polynomials
- How to Multiply a Polynomial and a Monomial
- How to Multiply Binomials
- How to Do Operations with Polynomials
- How to Factor Trinomials
- How to Divide Monomials