Enter Polynomial Inputs
Choose the highest degree, fill the coefficients, set an x value, and optionally generate a range table for graphing.
Formula Used
General polynomial:
P(x) = anxn + an-1xn-1 + ... + a1x + a0
Value at a chosen input:
Substitute the selected x into every term, then add all term values.
First derivative: P'(x) = n·anxn-1 + (n-1)·an-1xn-2 + ... + a1
This calculator evaluates each polynomial term directly, totals the result, computes the derivative, and builds a point table for plotting across your chosen range.
How to Use This Calculator
- Select the highest degree that matches your polynomial.
- Enter each coefficient from x8 down to the constant term.
- Type the x value where you want P(x).
- Set a start, end, and step size for the graph table.
- Click Calculate Polynomial Value to view the result, table, derivative, and chart.
Example Data Table
Example polynomial: P(x) = x3 - 2x2 + 3x - 5
| x | P(x) |
|---|---|
| -1 | -11 |
| 0 | -5 |
| 1 | -3 |
| 2 | 1 |
| 3 | 13 |
FAQs
1. What does this calculator find?
It substitutes a chosen x into your polynomial, calculates every term, adds them, and returns the final value. It also shows derivative output, graph points, and a results table.
2. What is a polynomial value?
A polynomial value is the numeric result after replacing x with a specific number. For example, if x = 2, each term uses 2 and the summed result becomes P(2).
3. Why does the calculator ask for degree?
The degree tells the calculator which highest power should be active. Coefficients above that degree are visually muted and ignored during the final calculation.
4. What does the derivative result mean?
The derivative measures how quickly the polynomial changes near your chosen x. A positive value means the graph rises there, while a negative value means it falls.
5. Why generate a table and graph range?
A range shows how the polynomial behaves across many x values instead of one point only. This helps you inspect turning patterns, steep changes, and approximate highs or lows.
6. Can I use decimals or negative numbers?
Yes. Coefficients, x values, and range settings accept decimals and negative numbers. That makes the calculator suitable for classroom work, checks, and modeling tasks.
7. What should I do if the graph fails?
Usually the step size is too small for the chosen range. Increase the step size or reduce the interval so the calculator produces a manageable number of plotted points.
8. What do the CSV and PDF options save?
CSV saves the generated x and P(x) table for spreadsheet use. PDF captures the visible result report, including summary cards, breakdown table, and graph section.