103 LearnersLast updated on June 25th, 2025
Polynomial Division Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re studying algebra, working on mathematical models, or solving equations, calculators will make your life easy. In this topic, we are going to talk about polynomial division calculators.
What is a Polynomial Division Calculator?
A polynomial division calculator is a tool to perform division operations on polynomials. Polynomial division can be complex and time-consuming, but with this calculator, you can easily divide one polynomial by another. This calculator makes the process much easier and faster, saving time and effort.
How to Use the Polynomial Division Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the polynomials: Input the dividend and divisor polynomials into the given fields.
Step 2: Click on divide: Click on the divide button to perform the division and get the result.
Step 3: View the result: The calculator will display the quotient and remainder instantly.
How to Divide Polynomials?
To divide polynomials, the calculator uses the process known as polynomial long division or synthetic division.
For example, divide (x3 + 2x^2 - 5x - 6) by (x - 2).
Step 1: Divide the first term of the dividend by the first term of the divisor to get the first term of the quotient.
Step 2: Multiply the entire divisor by this term and subtract from the original polynomial.
Step 3: Repeat the process with the new polynomial until the remainder is less than the degree of the divisor.
Tips and Tricks for Using the Polynomial Division Calculator
When using a polynomial division calculator, here are a few tips and tricks to make things smoother and avoid mistakes:
- Double-check your input to ensure the polynomials are entered correctly.
- Pay attention to the degree of the polynomials; the dividend should have a higher or equal degree compared to the divisor.
- Make sure to account for any missing terms in your polynomials by using a zero coefficient.
Common Mistakes and How to Avoid Them When Using the Polynomial Division Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible to make errors while using a calculator.
Mistake 1
Incorrectly entering the polynomial coefficients.
Ensure that all coefficients are entered correctly, including zero coefficients for missing terms. This helps in performing accurate calculations.
Mistake 2
Overlooking the remainder in polynomial division.
Always check if there is a remainder after the division. When dividing polynomials, the remainder should be of a lower degree than the divisor.
Mistake 3
Using the wrong division method.
Choose the appropriate method (long division or synthetic division) depending on the polynomials involved. Synthetic division is only applicable when the divisor is a linear polynomial.
Mistake 4
Not simplifying the quotient properly.
After getting the quotient, simplify it if possible. This step can sometimes be overlooked, leading to less precise results.
Mistake 5
Assuming the calculator will handle all polynomial division scenarios.
Be aware that some complex polynomial divisions might require additional steps or verification. Always double-check your results if they seem unusual.
Polynomial Division Calculator Examples
Problem 1
Divide (x^2 + 3x + 2) by (x + 1).
Use polynomial long division:
- Divide the first term (x2) by (x) to get (x).
- Multiply x by (x + 1) to get (x2 + x).
- Subtract x2 + x from (x2 + 3x + 2) to get (2x + 2).
- Divide 2x by x to get 2.
- Multiply 2 by (x + 1) to get 2x + 2.
- Subtract (2x + 2) from (2x + 2) to get 0.
- Quotient: (x + 2), Remainder: 0.
Explanation
By dividing (x2 + 3x + 2) by (x + 1), we obtain a quotient of (x + 2) with no remainder.
Problem 2
Divide (x^3 - 2x^2 + 4x - 8) by (x - 2).
Use synthetic division:
- Set up the coefficients: (1, -2, 4, -8) and (x - 2) gives us (2).
- Bring down the first coefficient (1).
- Multiply (2) by (1) and add to (-2) to get (0).
- Multiply (2) by (0) and add to (4) to get (4).
- Multiply (2) by (4) and add to (-8) to get (0).
Quotient: (x2 + 0x + 4), Remainder: (0).
Explanation
Using synthetic division, dividing (x3 - 2x2 + 4x - 8) by (x - 2) gives a quotient of (x2 + 4) with no remainder.
Problem 3
Divide \(2x^2 + 3x + 1\) by \(x + 2\).
Use polynomial long division:
- Divide (2x2) by (x) to get (2x).
- Multiply (2x) by (x + 2) to get (2x2 + 4x).
- Subtract (2x2 + 4x) from (2x2 + 3x + 1) to get (-x + 1).
- Divide (-x) by (x) to get (-1).
- Multiply (-1) by (x + 2) to get (-x - 2).
- Subtract (-x - 2) from (-x + 1) to get (3).
Quotient: \(2x - 1\), Remainder: \(3\).
Explanation
Dividing (2x2 + 3x + 1) by (x + 2) yields a quotient of (2x - 1) with a remainder of (3).
Problem 4
Divide (x^3 + 6x^2 + 11x + 6) by (x + 3).
Use polynomial long division:
- Divide (x3) by (x) to get (x2).
- Multiply (x2) by (x + 3) to get (x3 + 3x2).
- Subtract (x3 + 3x2) from (x3 + 6x2 + 11x + 6) to get (3x2 + 11x + 6).
- Divide (3x2) by (x) to get (3x).
- Multiply (3x) by (x + 3) to get (3x2 + 9x).
- Subtract (3x2 + 9x) from (3x2 + 11x + 6) to get (2x + 6).
- Divide (2x) by (x) to get (2).
- Multiply (2) by (x + 3) to get (2x + 6).
- Subtract (2x + 6) from (2x + 6) to get (0).
Quotient: \(x^2 + 3x + 2\), Remainder: \(0\).
Explanation
Dividing (x3 + 6x2 + 11x + 6) by (x + 3) results in a quotient of (x2 + 3x + 2) with no remainder.
Problem 5
Divide (3x^3 + x^2 - 4x + 5) by (x - 1).
Use synthetic division:
- Set up the coefficients: (3, 1, -4, 5) and (x - 1) gives us (1).
- Bring down the first coefficient (3).
- Multiply (1) by (3) and add to (1) to get (4).
- Multiply (1) by (4\) and add to (-4) to get (0).
- Multiply (1) by (0) and add to (5) to get (5).
Quotient: (3x2 + 4x + 0), Remainder: (5).
Explanation
Using synthetic division, dividing (3x3 + x2 - 4x + 5) by (x - 1) results in a quotient of (3x2 + 4x) and a remainder of (5).
FAQs on Using the Polynomial Division Calculator
1.How do you divide polynomials?
2.Can you always use synthetic division?
3.What happens if there is a remainder?
4.How do I use a polynomial division calculator?
5.Is the polynomial division calculator accurate?
Glossary of Terms for the Polynomial Division Calculator
- Polynomial Division Calculator: A tool used to divide one polynomial by another, providing the quotient and remainder.
- Polynomial Long Division: A method for dividing polynomials similar to long division with numbers.
- Synthetic Division: A simplified form of polynomial division used when the divisor is a linear polynomial.
- Quotient: The result obtained from the division of polynomials.
- Remainder: The part left over after division, which is smaller in degree than the divisor.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
