Expanded Form Polynomial Calculator

Multiply entered factors into expanded polynomial form. Review degree, coefficients, derivative, integral, and plotted behavior. Export clean results for lessons, homework, and revision tasks.

Calculator Inputs

Examples: x+2, 2x-5, x^2+3x+1

Example Data Table

This sample uses factors (x + 2)(x - 1)(x + 3). The expanded form is x^3 + 4x^2 + x - 6.

x P(x)
-30
-2-4
-1-4
0-6
10
220
360

Formula Used

Polynomial product:
P(x) = F1(x) × F2(x) × ... × Fn(x)
Coefficient convolution:
If A(x) = Σ ai x^i and B(x) = Σ bj x^j, then C(x) = A(x)B(x) has coefficient ck = Σ ai b(k-i).
Evaluation:
P(a) = Σ cn a^n
Derivative:
d/dx [cn x^n] = ncn x^(n-1)
Integral:
∫ cn x^n dx = cn x^(n+1)/(n+1) + C

How to Use This Calculator

  1. Enter up to four polynomial factors.
  2. Use one variable symbol consistently in every factor.
  3. Set the evaluation point and graph range.
  4. Choose the output order and rounding precision.
  5. Press Expand Polynomial to see the result above the form.
  6. Review the expanded form, derivative, integral, table, and graph.
  7. Download the generated summary as CSV or PDF.

Frequently Asked Questions

1. What does expanded form mean?

Expanded form shows every polynomial term separately after multiplication. It removes grouped factors and combines like powers into one simplified expression.

2. Can I enter decimal coefficients?

Yes. You can use decimals like 0.5x^2 or 2.75x. The calculator multiplies them, simplifies the result, and rounds displayed values using your selected precision.

3. Can I use one factor only?

Yes. A single factor still works. The calculator then formats that polynomial, evaluates it, creates a graph, and builds the coefficient table.

4. Does the tool combine like terms automatically?

Yes. Terms with the same exponent are merged after multiplication. That makes the final expanded polynomial clean and ready for algebra checks.

5. Why is my factor rejected?

Use simple polynomial input only. Avoid multiplication signs, fractions, or nested parentheses inside one factor. Accepted examples include x+2, 3x^2-4x+1, and 0.5x-7.

6. What does the graph represent?

The graph plots the expanded polynomial over your chosen x-range. It helps you inspect roots, turning behavior, and general growth patterns visually.

7. What is the coefficient table for?

The coefficient table lists each power and its matching coefficient. It is useful for checking standard form, copying into notes, or building further algebra steps.

8. Do the exports include the result table?

Yes. CSV and PDF exports include the main summary and generated x-value table, making it easier to save results for classwork or revision.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.