## How to Write Polynomials in Standard Form

Read,4 minutes

### What is a Polynomial?

A polynomial can be broken down into two words: "**poly**" and "**nomial**," which both signify many expressions, as suggested by the name of the concept. In mathematics, a polynomial is an algebraic or mathematical expression that has **at least **two terms that are linked together by a mathematical operation. It should be noted that expressions within the polynomial terms could be a **constant**, a **variable**, or even a **mixed **term that contains a **co-efficient**. A polynomial should also have the power of the variable (let's say \(x\)) be an integer rather than a fractional power such as the squared root or the cube root.

For example, \(7x^{\frac{1}{2}} \ - \ 5x \ + \ 13\) is **not **a polynomial as the first term has a **fraction power **of \(x\).

### Different 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. Also, monomials can all be mixed terms as well as just pure variable terms.**Ex**: \(5x^2, \ 6x^3, \ 69x\), etc.**Binomial**: Binomials consist of just**two terms**and they must have a mathematical operation in between. Binomials can have mixed terms, pure variable terms, or even pure constant terms in the expression.**Ex**: \(2x^2 \ + \ 5x^3, \ 3x^2 \ + \ 8y, \ xy^2 \ + \ 2x\), etc.**Trinomial**: Trinomial consist of**three terms**and between every two terms there is a mathematical operation. Trinomials too can have mixed terms, pure variable terms, and even pure constant terms in the expression. Ex: \(2x^2 \ + \ 3x \ + \ 10, \ 4x^3 \ + \ 3x^2 \ + \ 7, \ 3x^2y \ + \ 4xy \ + \ 6\), etc.

### Standard Form of Polynomials

The standard form of a polynomial function \(f(x)\) of the degree \(n\) is:

\(F(x) \ = \ a_{n}x^n \ + \ a_{n-1}x^{n \ - \ 1} \ + \ …… \ + \ a_{1}x \ + \ a_{0}\), where the first term is the term with the **biggest **power of the variable (in this case \(x\)).

To write a polynomial in the standard form, we **must **arrange all powers of \(x\) in **descending order**. For example, in \(4x^2 \ - \ 9x^3 \ + \ 13x \ - \ 7\), we write the **standard form **as:

\(-9x^3 \ + \ 4x^2 \ + \ 13x \ – \ 7\).

### Exercises for Writing Polynomials in Standard Form

**1) **\(-20x^2 \ - \ x \ + \ 24x^3 = \)

**2) **\(x \ -\ 2(9x^3 \ - \ x) \ - \ 13x^4 = \)

**3) **\(x \ -\ 2(16x^3 \ - \ x) \ - \ 20x^4 = \)

**4) **\(-3x^2 \ - \ 3 \ + \ 6x^3 = \)

**5) **\(-18x^2 \ - \ 7 \ + \ 19x^3 = \)

**6) **\(-2(7x^3 \ - \ x) \ - \ 9x^4 = \)

**7) **\(16x^2 - 18x^3 = \)

**8) **\(-2(22x^3 \ - \ x) \ - \ 24x^4 = \)

**9) **\(-5x^2 \ - \ x \ + \ 9x^3 = \)

**10) **\(-6x^2 \ - \ x \ + \ 10x^3 = \)

## Writing Polynomials in Standard Form 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