Multiply two factors
A = 1, −3, 2 and B = 1, 1 represent x² − 3x + 2 and x + 1. Their product is x³ − 2x² − x + 2.
Calculations run locally in your browser. This tool does not upload the numbers you enter.
How to use the Polynomial Calculator
- 01
Select an operation. Enter A as coefficients from highest power through the constant term.
- 02
For two-polynomial operations, enter B in the same format. For evaluation, enter x instead.
- 03
Calculate, inspect the expanded result, and copy or download the polynomial and coefficients.
Examples
Keep a missing term
The list 3, 0, −4 represents 3x² − 4. Its derivative is 6x, with descending coefficients 6, 0.
Coefficient order matters
The number of entries determines the degree before leading zeros are removed. A list of four coefficients represents a cubic, even if some middle entries are zero. Leading zeros are normalized away, while internal and trailing zeros preserve the positions of terms.
Arithmetic on lists
Addition and subtraction align like powers, padding the shorter list with leading zeros. Multiplication combines every pair of terms and adds their products in the matching output power. The derivative multiplies each coefficient by its exponent and reduces that exponent by one.
Evaluation and precision
Evaluation uses nested multiplication, also known as Horner’s method, rather than calculating each power separately. The tool handles real numeric coefficients and reports results to 12 significant digits. It does not parse expressions, factor polynomials, find general roots, or perform symbolic algebra.
What to know
- No expression evaluation, symbolic factoring, polynomial division, or arbitrary-precision coefficients.
Common questions
How do I enter a constant?
Use one value, such as 7. Its derivative is the zero polynomial, and its value is 7 for every supported x.
Can I type x² + 2x + 1?
Use 1, 2, 1 instead. Expression strings and function calls are not accepted.
What degree is supported?
Each input polynomial can have degree at most 20. Multiplying two degree-20 inputs can produce degree 40.
Are integer coefficients always exact?
These operations use JavaScript numbers. Small integer results are often exact, but large integer products and decimal results may round; use the coefficient output as a numerical result.