Enter Polynomial Details
Formula Used
This calculator raises a polynomial to a whole-number exponent by repeated polynomial multiplication, optimized with exponentiation by squaring.
General term rule: coefficients of matching exponents are added after each multiplication step.
Evaluation rule: after expansion, substitute the chosen variable value and sum all terms.
How to Use This Calculator
- Enter a single-variable polynomial such as
x^2 + 2x + 1. - Choose the whole-number exponent you want to apply.
- Optionally enter a variable value to evaluate the expanded result.
- Select the required decimal precision.
- Press the calculate button to view the expanded polynomial above the form.
- Download the coefficient table as CSV or save a PDF report.
Example Data Table
| Polynomial | Power | Expanded Result | Degree |
|---|---|---|---|
| x + 1 | 3 | x^3 + 3x^2 + 3x + 1 | 3 |
| 2x - 5 | 2 | 4x^2 - 20x + 25 | 2 |
| x^2 + 2x + 1 | 2 | x^4 + 4x^3 + 6x^2 + 4x + 1 | 4 |
| 3x^2 - x + 4 | 2 | 9x^4 - 6x^3 + 25x^2 - 8x + 16 | 4 |
Frequently Asked Questions
1. What does this calculator do?
It raises a single-variable polynomial to a whole-number power, expands the expression, lists coefficients, reports degree, and can evaluate the result at a chosen variable value.
2. What input format should I use?
Enter terms like 3x^2 - 2x + 7. Use one variable only, omit multiplication symbols if you like, and keep exponents non-negative.
3. Can I use decimal coefficients?
Yes. Values such as 1.5x^2 - 0.75x + 2 are supported. Choose decimal places to control the displayed output.
4. Does it support negative exponents?
No. This tool is designed for polynomial powers with whole-number exponents from zero through twenty.
5. Why is the result degree larger than the input degree?
The degree of the expanded result equals the original polynomial degree multiplied by the exponent, provided the leading coefficient is non-zero.
6. What happens when the exponent is zero?
Any non-zero polynomial raised to the zero power becomes 1, so the result is a constant polynomial with degree zero.
7. What do the CSV and PDF buttons export?
CSV downloads the exponent and coefficient table. PDF creates a compact report with the input, power, expanded form, degree, leading coefficient, and evaluation.
8. Why are like terms combined automatically?
Polynomial multiplication produces repeated exponents. Combining like terms gives the standard simplified form used in algebra, graphing, and further calculations.