How to Write an Equation or Polynomial in Standard Form

8 min read

How to Write an Equation or Polynomial in Standard Form

A polynomial is referred to as a standard form and it is the mathematical expression of one or more than one algebraic term. A polynomial expression includes variables, exponents, and constants, but they never include the negative exponents. Usually, polynomials contain different terms and exponents that are in descending order. It becomes challenging for a person when too small or large values are taken into account.

Simply, consider the standard form calculator that displays the number in the standard form, scientific e notation, and engineering notation also. The number might be integer form or decimal. A standard notation calculator is a considerable option because it makes the conversion faster and easier.

Definition of Polynomial:

In mathematics, a polynomial is said to be an expression that consists of single and multiple terms. The word polynomial is taken by combining two different terms and they are “Poly” and “Nominal”. In short, the polynomial expression has two or more than two algebraic terms and they are considered constants, coefficients, variables, exponents, and operators. Sometimes the very large and small values to standard form become very tricky.

So, make use of the “convert to standard form calculator” that not only converts the number to standard form. But the standard notation calculator also converts the number to Engineering notation, to scientific E-Notation, and real number format.

Standard Form in Polynomial Degree:

The degree of the polynomial is said to be the value of the large exponents in the polynomial. However, it is different when the single variable and multivariable polynomial are taken into account. In the single-variable polynomial, the degree of the polynomial is said to be the highest power of a variable. While the degree of the polynomial is the sum of all the powers of the polynomial when you are dealing with the multivariable polynomials.

Writing an equation standard form is a daunting task but thanks to the standard form calculator that the process is easier. The standard form equation calculator is a handy online tool that allows you to write the equation in standard form within a fraction of seconds.

Steps to Writing a Polynomial in Standard Form:

Below are the six simple steps that can help you in writing down the polynomial in standard form:

  • Write down the term that you want to write.
  • Make a group of all the similar terms.
  • Then, find the exponent.
  • After finding the exponents, write the term with the highest exponent.
  • Now, write down the rest of the terms in descending order.
  • In the last step, write the constant terms at the end. Here, constant terms represent the numbers that are without the variables.

By following the listed above steps you can easily write the equation of polynomial in standard form. Instead of using this long and time-consuming procedure, you can use the standard form calculator that allows you to write the polynomial equation in its ordinary form.

Types of Polynomial:

Polynomials are categorized depending on the degree and their power. Polynomials have three different types depending on the number of terms and they are monomials, binomials, and trinomials.

Monomial:

A monomial is known as an algebraic expression that consists of only one term. It could be a term, number, product, or a variable of a number & variable along with an exponent. The number section of the term is known as the coefficient.

Binomials:

In mathematics, binomials are expressions that are based on two terms. A binomial in the single indeterminate can be written in the form: cxm – dxn. Where a and d represent the numbers while m & n are distinct nonnegative integers and s is said to be the symbol that is called an indeterminate or a variable for its historical reasons. The listed below are the requirements that a binomial must have:

  • Exponents must be different if the variable is the same.
  • Binomials must have two terms.
  • Exponents of the binomials must be positive integers and they can be in negative or fraction form.

Trinomial:

An algebraic expression along with the three terms and consists of constants and variables of one or more terms. The expression utilizes the arithmetic operators and symbols for the separators like ×, ÷, +, and -. Monomial, polynomial, binomial, and trinomial are categorized under the algebraic expression.

Addition and Subtraction of Polynomials in Standard Form:

We use the two basic arithmetic operations to increase or decrease the value of the polynomials. The basic operators are addition and subtraction. Whatever your requirements are whether you want to add the numbers or add the polynomials the basic rules remain the same for it. The difference is just that when you add the numbers you need to align the appropriate place values and carry out the operation.

You are required to pair up similar terms and then add them at the time of dealing with the addition and subtraction of polynomials. The rules for the addition and subtraction from the numbers are translated over to the polynomials. Writing down the numbers and equations in the standard form is difficult when you do it manually. However, you can write the equation in the standard form with the free assistance of an online standard form calculator.

Method: How to Write in Standard Form?

There are different rules for all types of conversion that you can keep in mind while dealing with polynomials. For instance: for converting a number in the standard form, we need to follow a few rules but the same rules are not required for the conversion of polynomials in standard notation to scientific form. In this section, we are going to explain all the methods for converting the number of the equation in its standard form. If you don’t want to follow these methods then, you can make use of an online standard form calculator for the conversions.

Let’s First Discuss How to Convert the Linear Equation in Standard Form:

The linear equation in the standard form is represented as ax + by = c. The first step to write the linear equation is to write the equation in the format that we mentioned before this sentence. Now, the below listed are a few of the main points that you need to consider at the time of converting the linear equations to their standard form.

  • The “A” constant can’t be negative.
  • A & B constants can not be zero
  • And the values of a, b, and c must have to be the integers.

If this procedure for linear equations seems to be difficult or you think that this will be a time-consuming process then, you can try a standard notation calculator that displays the results for your given inputs with the blink of an eye.

Writing the Polynomials in Standard Form:

The logic behind the standard form of the polynomial is to start by using the component along with the highest degree and here the exponent of a variable is referred to as a degree. Convert the polynomial into its standard form by using the degree of each element. Now, arrange the equation in descending order. In this way, you can easily write the number/equation in the standard form. Instead of this method for writing the polynomials using an online standard form calculator is a considerable option.

Method for Quadratic Equation:

The quadratic equation is represented in the standard form as shown below:

Ay2 + By + c = o

To understand the method of converting the quadratic equation into the standard form use the below-listed steps:

  • To convert the quadratic equation, you need to compute the left-hand side of the equation.
  • Now multiply the variable by the expression of the equation
  • Rearrange the equation and set aside the similar constants on the left side of the equation. By arranging similar constants you can get the desired constant numbers.

No doubt, this one method is more complex as compared to the other mentioned methods. But if you follow these steps carefully then, you can easily write the equation or polynomials in standard form. You can also consider using the standard form calculator that can convert any into the scientific-e-notation, real number, and also in standard form. This standard notation calculator will also save your time by making quick calculations.

Conclusion – How to Write an Equation or Polynomial in Standard Form

In this guidepost, the hot topic of discussion is “how to write the equation & polynomial in standard form. The procedure to write the equation is complex and time-consuming as well. but by using our guidelines you can easily compute the number in standard form. We have mentioned three different methods in the article that can help you to write the number/ equation in different cases.

If the listed methods are still trick for you then, you have to use the standard form calculator that can quickly convert the number in scientific notation with the blink of an eye. The methods that we discussed in the article may vary depending on the equation type. So, use these methods according to the requirement of the equation to write them correctly in standard form.

 

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