Enter Polynomials
Supported format: single-variable polynomials with whole numbers or decimals. Example: 2.5x^3 - x + 6. Negative exponents are not included.
Formula Used
Polynomial addition works by combining coefficients attached to equal exponents.
P(x) = Σ aₖxk
Q(x) = Σ bₖxk
P(x) + Q(x) = Σ (aₖ + bₖ)xk
For every exponent k, the calculator adds the matching coefficients. Missing terms are treated as zero before the final expression is simplified.
How to Use This Calculator
- Enter the first polynomial in standard algebraic form.
- Enter the second polynomial using the same variable symbol.
- Set the variable, decimal precision, and preferred term order.
- Press Add Polynomials to calculate the simplified sum.
- Review the result card, combined-coefficient table, and working steps.
- Use the CSV or PDF buttons to export the result summary.
Example Data Table
| Example | Polynomial 1 | Polynomial 2 | Simplified Sum |
|---|---|---|---|
| 1 | 3x^2 + 4x + 5 | 2x^2 - x + 7 | 5x^2 + 3x + 12 |
| 2 | x^4 - 2x + 9 | -3x^4 + 8x - 1 | -2x^4 + 6x + 8 |
| 3 | 0.5x^3 + 1.25x | 1.5x^3 - 0.25x + 2 | 2x^3 + x + 2 |
Frequently Asked Questions
1. What does this calculator add?
It adds two single-variable polynomials by matching equal exponents, combining coefficients, and rebuilding the simplified result in your chosen display order.
2. Can I use decimal coefficients?
Yes. Decimal values such as 2.5x^3 or 0.75x are accepted. The precision setting controls how many decimal places appear in formatted output.
3. Does term order matter in the input?
No. You can enter terms in mixed order. The calculator reads each exponent, groups like terms, then displays the final sum in ascending or descending order.
4. Can it add polynomials with missing terms?
Yes. Missing powers are treated as zero. For example, if one polynomial lacks an x^2 term, its x^2 coefficient is assumed to be zero.
5. Are different variables allowed together?
No. Both expressions must use one shared variable symbol. Mixing x and y in the same calculation is not supported in this version.
6. What happens if terms cancel out?
If opposite coefficients sum to zero, that term disappears from the simplified result. If every term cancels, the calculator returns the zero polynomial.
7. What do the export buttons include?
The CSV export saves the coefficient table. The PDF export creates a printable summary showing both inputs, the simplified sum, and the combined like-term table.