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Long Division of Polynomials Calculator + Online Solver With Free Steps
Long Division Calculator is a helpful tool that allows you to calculate the remainder and quotient for the division of polynomials. Division of polynomials is one of algebra’s most fundamental and essential parts.
The calculator helps you find the remainder and quotient with complete steps and the details of calculations for the long polynomial division. It clarifies the whole concept of how to do long division of polynomials.
Polynomials can be divided by using different methods. But this calculator applied the long division method to find the results. This method is used widely to divide polynomials as it breaks down the complex polynomials forms into the simplest form.
Long Division is the best method to divide two long polynomials. There can be four types of long divisions that can be performed. These are:
Polynomial Division by a monomial
Polynomial Division by nominal
Polynomial Division by Binomial
Polynomial Division by another Polynomial
The Long division of polynomials calculator solves all these types of divisions with complete steps and calculations.
The calculator requires the dividend and divisor polynomial as the input elements and returns the quotient and remainder after the long division.
What Is a Long Division of Polynomials Calculator?
A long division of polynomials calculator is an online calculator that can be used to find the remainder and quotient of the polynomials. It performs a long division of the given dividend and divisor.
You can calculate the remainder and quotient very quickly using this tool without extra effort. This calculator does not need prior purchasing, downloading, installation, etc. It can be used in any good browser and is available 24/7.
It provides you with the most accurate and simplified result of polynomial division. Anyone with a good internet connection can use this calculator anywhere. It can be used on both mobile devices and desktops or laptops.
It is a free tool with no limit on the number of times you can use it. It has a straightforward interface and is self-explanatory.
In the next sections, you will find the procedure of using this calculator, its working mechanism, and solved examples. Please keep reading to get full advantage out of it.
How To Use the Long Division of Polynomials Calculator?
You can use the Long division of polynomials calculator by inserting the dividend polynomial and divisor polynomials in the given boxes. It is a calculator with a user-friendly interface that contains only two input boxes and a click button for result processing.
There is a very short concise, and easy procedure for using the calculator. You just need to follow the steps mentioned below to get the proper results.
Step 1
Enter the Dividend in the first box labeled as divide. Remember that the dividend polynomial is the polynomial to be divided into some parts.
Step 2
In the second box, labeled as ‘by,’ enter the divisor polynomial. Divisor polynomial divides the polynomial, or it’s a polynomial by which the other polynomial is to be divided.
Output
The calculator’s output is displayed in a new window that pops up when you press the submit button.
The output interface is divided into two sections. The first section shows the input values, and the second shows the result.
The quotient and remainder are highlighted within a box.
How Does the Long Division Calculator Work?
The Long division of the polynomial calculator works by calculating the remainder and quotient for the polynomial division. It requires two inputs, dividend and divisor polynomial, for calculation.
It works by implementing a long division procedure step by step and, after calculations, gives the remainder and quotient using two input elements.
What Is a Polynomial?
A polynomial is an algebraic expression consisting of different variables, constants, and exponents. These variables, constants, and exponents are combined using one or many types of mathematical operations such as subtraction, addition, division, and multiplication.
Let us understand polynomials by taking an example:
7x$^ 2$ + 3 = 0
In the given equation, there are specific terms that we need to understand. Here, x is known as the variable, 7, multiplied by x 2 and has a unique name known as a coefficient, and 3 in the equation is known as the constant.
Polynomials can also be categorized into three categories: monomial, binomial, and trinomial, based on the number of terms present in an algebraic expression.
What Is the Degree of the Polynomial?
The degree of the polynomial in an equation is the highest power of the variable in that algebraic equation. In other words, the highest exponential is known as the degree of the polynomial and depending upon the degree of polynomials; they are classified into categories.
The major categories are:
- Constant or zero polynomial
- Linear polynomial
- Quadratic polynomial
- Cubic polynomial
- Quartic polynomial
Polynomial Long Division Method
The polynomial long division method divides a polynomial with another polynomial of the same or lower degree and breaks down the complex polynomial forms into the simplest form.
This calculator applied the long division method to find the results. This is the most used method for the division of long polynomials. It performs a long division of the given dividend and divisor. In a long division, you must divide the dividend’s leading term by the divisor’s leading term. Then multiply the result with the divisor. Subtract the remainder from the obtained result.
Keep doing these steps until your remainder’s degree is less than your divisor’s. When the degree of remainder is less than the degree of the divisor, you will get the remainder. It will be more apparent by understanding the solved examples.
Depending upon the type of the second expression, we can categorize it into four types of long division of polynomials given as follows:
- Polynomial Division by a monomial
- Polynomial Division by nominal
- Polynomial Division by Binomial
- Polynomial division by another polynomial
Solved Examples
An excellent way to understand the tool is to solve the examples and analyze them. Some examples are described below that are solved using the Long Division Polynomial Calculator.
Example 1
Luna wants to divide the polynomial x$^3$ – 6x$^2$ + 5x – 3 by x – 2. Can you help her with the solution using a long-division polynomial calculator?
Solution
The calculator calculates the results using the given dividend and divisor.
Here, the polynomial is given as:
x$^3$ – 6x$^2$ + 5x – 3
It is divided by x – 2.
Divide the leading term of dividend with the leading term of divisor as:
x$^3$ / x = x$^2$
Multiply it with a divisor:
x$^2$ x (x – 2) = x$^3$ – 2x$^2$
Now subtract the dividend from the obtained result:
( x$^3$ – 6x$^2$ + 5x – 3 ) – ( x$^3$ – 2x$^2$ ) = – 4x$^2$ + 5x -3
Repeat these three steps. Divide the leading term of dividend with the leading term of divisor:
-4x$^2$ / x = – 4x
Multiply it with a divisor:
-4x x (x – 2) = – 4x$^2$ + 8x
Now subtract the dividend from the obtained result:
(- 4x^2 + 5x -3) – (- 4x^2 + 8x) = -3x -3
Again, divide the leading term of dividend with the leading term of divisor:
-3x / x = -3
Multiply it with a divisor:
-3 x (x – 2) = -3x + 6
Now subtract the dividend from the obtained result:
( -3x – 3) – ( -3x + 6) = – 9
Keep doing these three steps until your remainder’s degree is less than your divisor’s degree.
So the calculator gives the result as follows:
Quotient = x^2 – 4x – 3
Remainder = – 9
Example 2
Kane wants to divide the polynomial 2x$^3$ – 4x$^2$ + 2x – 2 by x – 3. Can you help her with the solution using a long-division polynomial calculator?
Solution
The calculator calculates the results using the given dividend and divisor.
Here, the polynomial 2x$^3$ – 4x$^2$ + 2x – 2 is divided by x – 3.
Start Division as:
2x$^3$ / x = 2x$^2$
2x$^2$ x (x – 3) = 2x$^3$ – 6x$^2$
Now subtract the dividend from the obtained result:
( 2x$^3$ – 4x$^2$ + 2x – 2 ) – ( 2x$^3$ – 6x$^2$ ) = 2x$^2$ + 2x -2
Repeat these three steps again.
2x$^2$ / x = 2x
2x x (x – 3) = 2x$^2$ – 6x
( 2x$^2$ + 2x -2 ) – ( 2x$^2$ – 6x ) = 8x – 2
Again, divide the leading term of dividend with the leading term of divisor:
8x / x = 8
Multiply it with a divisor:
8 x (x – 3) = 8x – 24
Now subtract the dividend from the obtained result:
( 8x – 2 ) – ( 8x – 24 ) = 22
Keep doing these three steps until your remainder’s degree is less than your divisor’s degree.
Therefore, the results obtained using a calculator are given as follows:
Quotient = 2x^2 + 2x + 8
Remainder = 22