Calculator Inputs
Enter coefficients for up to three polynomials, choose the working degree, then calculate the summed expression and related values.
Formula Used
Base polynomials
P(x) = Σ aixi, Q(x) = Σ bixi, R(x) = Σ cixi
S(x) = P(x) + Q(x) + R(x)
Coefficient-by-coefficient sum
For each matching power i, the summed coefficient is si = ai + bi + ci.
Evaluation at x
S(x0) = Σ six0i
Derivative of the sum
S′(x) = Σ i·sixi-1 for all i ≥ 1
Definite integral over [a, b]
∫ S(x)dx from a to b = Σ [si / (i + 1)] · (bi+1 - ai+1)
How to Use This Calculator
Choose the working degree first. The calculator will only use coefficients from that degree down to the constant term.
Enter the coefficient for each visible term in Polynomial A, Polynomial B, and Polynomial C. Leave unused terms as zero.
Provide an x value to evaluate the summed polynomial numerically. This produces S(x) and S′(x) at the same point.
Set the lower and upper bounds if you want the definite integral of the summed polynomial across an interval.
Adjust the graph range and point count to control the Plotly chart. Wider ranges help visualize end behavior clearly.
Press calculate to show the result section above the form. Export the summary later as CSV or PDF.
Example Data Table
This sample uses degree 3, x = 2, and integral bounds [0, 2].
| Term | Polynomial A | Polynomial B | Polynomial C | Summed Coefficient |
|---|---|---|---|---|
| x^3 | 2 | 1 | -1 | 2 |
| x^2 | -3 | 5 | 2 | 4 |
| x^1 | 4 | -2 | 1 | 3 |
| x^0 | 1 | 6 | -4 | 3 |
Summed polynomial: S(x) = 2x^3 + 4x^2 + 3x + 3
S(2): 41
S′(2): 43
Integral from 0 to 2: 30.666667
FAQs
What does this calculator add together?
It adds up to three polynomials by matching like powers of x. Each coefficient is summed term by term to create one simplified result.
Can I use negative and decimal coefficients?
Yes. The inputs accept positive numbers, negative numbers, and decimals. That makes the tool suitable for classroom problems, engineering models, and numerical analysis work.
Why do some coefficient fields disappear?
The visible fields follow the selected polynomial degree. Choosing degree 3 hides x^8 through x^4 because they are not part of the active calculation.
What is the degree of the summed polynomial?
It is the highest power of x with a nonzero coefficient after addition. If higher terms cancel out, the final degree may be lower than expected.
Why is evaluation at x useful?
Evaluating at x converts the symbolic polynomial into a single number. This helps compare outputs, test points, and verify algebraic work quickly.
What does the derivative result represent?
The derivative shows the instantaneous rate of change of the summed polynomial. The calculator also evaluates that derivative at your chosen x value.
What is the purpose of the definite integral?
The definite integral measures the accumulated area contribution of the summed polynomial across the chosen interval. It is useful for analysis and applied math problems.
What do the export buttons contain?
The CSV file stores the summary and coefficient table. The PDF file includes the key results and the same coefficient breakdown for sharing or records.