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Adding and Subtracting Polynomials Calculator + Online Solver With Free Steps

An Adding and Subtracting Polynomials Calculator is an online widget that helps to perform addition and subtraction between two polynomials. Polynomials are expressions that have multiple terms joined together through some operation.

The calculator has a simple interface that takes the two polynomials as input, performs the specified operation, and returns the resultant polynomial expression.

What Is the Adding and Subtracting Polynomials Calculator?

The Adding and Subtracting Polynomials Calculator is an online calculator that can be used to add and subtract two polynomials

It is effortless to perform these basic two operations on simple polynomials with fewer terms but when the number of terms increases it becomes difficult to handle such expressions and the operations between them.

To tackle the operations between complex expressions, you can use this superb calculator that performs addition and subtraction in less than a second. It achieves state-of-the-art performance by giving perfect and error-free solutions.

Everyone can solve their problems using this calculator on their browser at all times. Also, this advanced tool is free, you don’t need to buy any subscriptions to get its premium features.

One of the algebraic expressions that we use the most consistently in daily life is the polynomial. They are used in geometry for representing functions, determining relations between two electrical parameters, for calculating profit and loss in business.

Moreover, they are used in finding the composition of solutions in chemistry, expressing the object motion in physics, and as feature functions in machine learning. So in short, polynomials are a fundamental element in every field.

That is why we offer you this tool that easily adds or subtracts any kind of polynomial. You can get further information on the use and working phenomena of this calculator in the coming sections.

How To Use the Adding and Subtracting Polynomials Calculator?

You can use the Adding and Subtracting Polynomials Calculator by entering the various polynomials and selecting the operation. The calculator can perform two operations which are addition and subtraction.

You must follow the given guidelines completely to solve your problem while using the calculator. The steps are described below.

Step 1

Enter the first polynomial of your problem in its respective box.

Step 2

Select one of the two available operations according to the problem in the Operation tab.

Step 3

Now put the second polynomial in the last empty field specified for it.

Step 4

Lastly, press the Calculate button to attain the final result. The result is itself a polynomial expression after operating input polynomials.

How Does the Adding and Subtracting Polynomials Calculator Work?

This calculator works by adding or subtracting the given polynomials based on the rules of addition and subtraction of numbers. The polynomials can be linear, quadratic, or cubic.

We should have knowledge about the polynomials for a better understanding of this calculator.

What Are the Polynomials?

An algebraic expression in which exponents of all the variables are whole numbers is called a Polynomial. It includes variables, coefficients, and constants. The word polynomial is made up of two words “poly” and “nomial” which means several terms.

The polynomial in standard form is expressed in decreasing order of exponents. The highest degree term is written first followed by the next highest degree term. The standard form of a polynomial is shown below:

\[a_{n}x^n+a_{n-1}x^{n-1}+….+a_{2}x^2+a_{1}x+a_{0}\]

The types of polynomials are classified into two categories. The first category is based on their degree and the second category is based on the number of terms.

Types of Polynomial Based on Degree

The degree of the polynomial is equal to the highest exponent of the variable in the polynomial. The polynomials are divided into the following four types, which are given below.

Zero Polynomial

The polynomials that have zero degrees mean that all the variables have zero power are called zero polynomials. They are also called constants.

Linear Polynomial

If the variable with the highest exponent of one is present in polynomial expression, then those expressions are called linear polynomials.

Quadratic Polynomial

The polynomials with the highest degree equal to two are called quadratic polynomials. In these polynomials, at least one variable has the power equal to two.

Cubic Polynomial

These are the polynomials that have at least one variable with an exponent equal to three.

Types of Polynomial Based on Terms

The polynomials are classified into the following types based on the number of terms.

Monomials

The polynomial expression with only one term is called Monomial.

Binomials

Binomial is the polynomial expression that has two unlike terms.

Trinomials

The polynomial expression that has three unlike terms is called Trinomial.

Adding and Subtracting Polynomials

The addition or subtraction of polynomials is based on the like and unlike terms. The terms which have similar variables and exponents are called the Like terms. However, those terms whose variables or exponents or both are not the same are called the Unlike terms.

The addition of polynomials is performed on like terms. The unlike terms can not be added together. The signs of the polynomials remain unchanged while performing the addition. The polynomials should be in their standard form and then perform addition on both the expressions.

The subtraction of the polynomials is also similar to addition. The subtraction is also performed on the like terms because unlike terms can not be subtracted. The polynomials should be arranged in standard form for subtracting them.

The difference between the addition and subtraction of polynomials is that in subtraction, the signs of all terms of subtracting polynomial are altered. The positive sign (+) changes to the negative sign (-) and vice versa.

There are two methods to perform the addition and subtraction of polynomials. The first method is to arrange them horizontally next to each other and then perform the addition or subtraction according to the rules mentioned above.

The second method is to position the polynomials vertically with the like terms placed one above the other and then subtract both the polynomials. This method is useful when there are complex expressions.

Solved Examples

Let’s explore some problems solved using the Adding and Subtracting Polynomials Calculator.

Example 1

A pharmaceutical scientist is working on the production of new medicine. To prepare it, he needs to add two different solutions made up of distinct ingredients. The composition of both solutions is represented by the following functions.

\[ s_{1}(x) = 5x^{4} + 8x^{3} + 0.5x^{2} + 9x \]

\[ s_{2}(x) = 2x^{3} + 1.25x^{2} + 6x \]

Add to get the polynomial expression for the new medicine.

Solution

The solution is obtained by adding those variable terms that have the same powers in both expressions.

\[ 5x^{4} + 10x^{3} + 1.75x^{2} + 15x \]

Example 2

Subtract the following two polynomial expressions.

\[7x^3+y^2-8z^2-6\]

\[3y^2-2z^2-4\]

Solution

The subtraction can easily be performed by inserting both the expressions in the calculator and selecting the subtraction operation. The resulting expression is given as:

\[-6z^2-2y^2+7x^3-2\]

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