Polynomial Calculator
Add, subtract, multiply, and evaluate polynomials with step-by-step solutions
About the Polynomial Calculator
A polynomial calculator is a powerful tool for performing various operations on polynomials, including addition, subtraction, multiplication, and evaluation. This calculator helps students and professionals work with polynomials efficiently while showing detailed step-by-step solutions.
What is a Polynomial?
A polynomial is an algebraic expression consisting of variables and coefficients, combined using addition, subtraction, and multiplication. Each term contains a variable raised to a non-negative integer power. For example: 2x² + 3x - 5 is a polynomial with three terms.
Polynomial Operations
- Addition: Combine like terms by adding their coefficients
- Subtraction: Distribute the negative sign and combine like terms
- Multiplication: Use the distributive property to multiply each term
- Evaluation: Substitute a value for x and calculate the result
How to Use This Calculator
- Enter your first polynomial using standard notation (e.g., 2x^2 + 3x - 5)
- Select the operation you want to perform
- Enter the second polynomial or evaluation point
- View the result and step-by-step solution instantly
Frequently Asked Questions
How do I enter a polynomial?
Use the caret symbol (^) for exponents. For example, enter "2x^2 + 3x - 5" for 2x² + 3x - 5. You can use spaces for readability, but they're not required.
What operations can this calculator perform?
This calculator can add, subtract, and multiply polynomials. It can also evaluate a polynomial at a specific point by substituting the value for x and calculating the result.
What is standard form for a polynomial?
Standard form arranges polynomial terms in descending order of exponents. For example, 3x³ + 2x² - 5x + 7 is in standard form, with powers decreasing from left to right.
How do you add polynomials?
To add polynomials, combine like terms by adding their coefficients. Like terms have the same variable raised to the same power. For example, 3x² and 5x² are like terms and add to 8x².
How do you multiply polynomials?
Use the distributive property to multiply each term of the first polynomial by each term of the second polynomial. Then combine like terms in the result. This is sometimes called the FOIL method for binomials.
Can I use this calculator for homework?
Yes! This calculator is perfect for checking your homework answers and understanding the step-by-step process. Use it to verify your work and learn the proper methods for polynomial operations.
What is evaluating a polynomial?
Evaluating a polynomial means substituting a specific value for the variable x and calculating the numerical result. For example, evaluating 2x² + 3x - 5 at x = 2 gives 2(2²) + 3(2) - 5 = 9.
Does this calculator handle fractions and decimals?
Yes, you can enter coefficients as decimals. The calculator will process them and display results accurately. For fractions, you can enter them as decimals (e.g., 0.5 for 1/2).
Related Calculators
Adding Polynomials Calculator
Add polynomials with color-coded like terms
Subtracting Polynomials Calculator
Subtract polynomials step-by-step
Multiplying Polynomials Calculator
Multiply polynomials using distribution or grid method
Polynomial Long Division Calculator
Divide polynomials with full long division layout
Synthetic Division Calculator
Fast polynomial division by (x - c)
Factor Theorem Calculator
Test if (x - c) is a factor of a polynomial