Computer Algebra Systems Calculator

Calculator

Operation

x Value

Decimal Precision

Graph Minimum x

Graph Maximum x

Graph Steps

Polynomial A Coefficients

Enter coefficients from highest power to constant.

Polynomial B Coefficients

Used for add, subtract, and multiply operations.

Quick Notes

Polynomial A example: 1, -3, 2 means x² - 3x + 2.

Polynomial B example: 2, 0, -5 means 2x² - 5.

For evaluate, the graph still plots the chosen expression.

Example Data Table

Case	Operation	Polynomial A	Polynomial B	x Value	Expected Output
1	Simplify	1, -3, 2	0	2	x^2 - 3x + 2
2	Evaluate	1, -3, 2	0	2	P(2) = 0
3	Derivative	3, 0, -4	0	1	6x
4	Integral	2, 6	0	0	x^2 + 6x + C
5	Multiply	1, -1	1, 1	0	x^2 - 1

Formula Used

Polynomial model: P(x) = a_nxⁿ + a_n-1x^n-1 + ... + a₁x + a₀.

Evaluation: Horner form reduces repeated multiplication and improves performance for large coefficient sets.

Derivative: d/dx(a_kx^k) = k a_kx^k-1.

Integral: ∫a_kx^kdx = a_kx^k+1/(k+1) + C.

Addition and subtraction: combine matching powers term by term.

Multiplication: distribute every term across every other term, then combine like powers.

How to Use This Calculator

Choose the symbolic operation you want to perform.
Enter Polynomial A coefficients in descending powers of x.
Enter Polynomial B only for add, subtract, or multiply.
Provide an x value when you want a numeric evaluation.
Set graph limits and graph steps for the plotted expression.
Click Calculate to show the result above the form.
Use the CSV and PDF buttons to export the current result.

FAQs

1. What does this calculator accept?

It accepts polynomial coefficients entered from highest power to constant. This keeps input reliable and makes symbolic operations fast and easy to validate.

2. Can it simplify general typed expressions?

This version focuses on polynomial coefficient input. It behaves like a practical algebra engine for common polynomial tasks rather than a full free-form symbolic parser.

3. Why are coefficients entered as lists?

Coefficient lists remove syntax ambiguity. They also make addition, subtraction, multiplication, differentiation, integration, and evaluation straightforward in one consistent interface.

4. How are roots computed?

Linear and quadratic cases use direct formulas. Higher-degree results are estimated numerically across the graph range, so some roots outside that range may not appear.

5. What does the graph show?

The graph plots the active expression for the chosen operation. For derivatives and integrals, it shows the transformed result, not only the original input.

6. What is the best graph step value?

Use more steps for smoother curves and sharper detail. Lower values are faster, while higher values improve visual accuracy on wider ranges.

7. What goes into the CSV and PDF files?

Both exports include the selected operation, input expressions, computed result, formula summary, root information, graph range, and chosen precision.

8. Is this useful for teaching and checking work?

Yes. It is suitable for classroom demonstrations, homework checking, and fast verification of polynomial transformations and numeric values.