Polynomial Algebra Calculator

Simplify, compare, and evaluate expressions using polynomial tools. Review coefficients, degrees, remainders, and derivatives clearly. Export every result quickly for reports, study, or sharing.

Enter Polynomial Inputs

Use variable x. Example formats: x^3-2x+5, 2x^2+x-1, 4.5x^4-3x+8.

Required. Main expression used for all calculations.
Optional. Enables pairwise algebra and division.
Optional. Numeric input such as 2, 3.5, or -1.
Controls displayed rounding for results and exports.

Example Data Table

Example Item Value
Polynomial A x^3 - 2x + 5
Polynomial B 2x^2 + x - 1
x Value 3
A + B x^3 + 2x^2 - x + 4
A - B x^3 - 2x^2 - 3x + 6
A × B 2x^5 + x^4 - 5x^3 + 8x^2 + 7x - 5
Derivative of A 3x^2 - 2
A(3) 26

Formula Used

1. Polynomial Addition

Add like terms with the same exponent: (aₙxⁿ + bₙxⁿ) = (aₙ + bₙ)xⁿ.

2. Polynomial Subtraction

Subtract matching coefficients by exponent: (aₙxⁿ - bₙxⁿ) = (aₙ - bₙ)xⁿ.

3. Polynomial Multiplication

Multiply each term in A by each term in B, then combine like powers: (ax^m)(bx^n) = abx^(m+n).

4. Polynomial Division

Long division uses the leading term ratio repeatedly until the remainder degree becomes smaller than the divisor degree.

5. Derivative

Differentiate each term using d/dx [ax^n] = anx^(n-1).

6. Indefinite Integral

Integrate each term using ∫ ax^n dx = a·x^(n+1)/(n+1) + C, for n ≠ -1.

7. Evaluation at x

Substitute the chosen x value into the polynomial and sum all term values.

How to Use This Calculator

Step 1

Enter Polynomial A using standard algebra form with variable x.

Step 2

Optionally enter Polynomial B when you want addition, subtraction, multiplication, or division results between two expressions.

Step 3

Optionally enter an x value to evaluate each polynomial numerically.

Step 4

Choose decimal precision to control how many digits appear in the displayed results.

Step 5

Click the calculate button. The result section will appear below the header and above the form.

Step 6

Use the CSV or PDF buttons to export the result summary for study notes, reports, or documentation.

Frequently Asked Questions

1. What input format should I use?

Use standard polynomial notation with x, such as x^3-2x+5 or 4x^4+0.5x^2-7. Avoid multiplication symbols and brackets.

2. Is Polynomial B required?

No. Polynomial B is optional. You only need it for pairwise operations like addition, subtraction, multiplication, and division.

3. Can I evaluate the polynomial at a number?

Yes. Enter any numeric x value, including decimals or negatives, and the calculator will compute A(x) and B(x) when available.

4. Does the calculator simplify like terms?

Yes. Matching exponents are combined automatically, so repeated powers are reduced into one clean coefficient per degree.

5. How does division work here?

The calculator uses polynomial long division. It returns both quotient and remainder unless the divisor is the zero polynomial.

6. Does it support derivatives and integrals?

Yes. It differentiates and integrates each term of the entered polynomial and displays the indefinite integral with + C.

7. Can I export my results?

Yes. After calculation, use the CSV button for spreadsheet-style output or the PDF button for a clean shareable file.

8. What are the current limits?

This version accepts one-variable polynomials in x with non-negative integer exponents. It does not process trigonometric or fractional-power expressions.

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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.