Calculator
Supported forms include constants, products, grouped powers, and implicit multiplication like 3x^2, 2xy, or (x+1)^3.
Plotly Graph
This chart summarizes the structure of the submitted expression.
Example Data Table
| Expression | Classification | Degree |
|---|---|---|
3x^2 - 5x + 7 |
Polynomial | 2 |
(x + 1)^3 |
Polynomial | 3 |
4xy + 2y^2 - 8 |
Polynomial | 2 |
1/x + 3 |
Not polynomial | — |
sqrt(x) + 2 |
Not polynomial | — |
x^(1/2) + 1 |
Not polynomial | — |
sin(x) + x |
Not polynomial | — |
5 |
Polynomial | 0 |
Formula Used
An algebraic expression is polynomial when every term follows this structure:
a · x₁^n₁ · x₂^n₂ · ... · xₖ^nₖ
Here, a is a real constant. Every exponent n must be a non-negative integer.
The total degree is the largest sum of exponents in any term.
Degree = max(n₁ + n₂ + ... + nₖ)
Expressions fail the test when variables appear in denominators, inside named functions, or with negative or fractional exponents.
How to Use This Calculator
- Enter your expression in the input field.
- Use
^for exponents, such asx^3. - Add parentheses for grouped powers, like
(x+1)^2. - Click Determine Now to analyze the expression.
- Read the result, degree, variables, and decision notes.
- Use the export buttons to save the result as CSV or PDF.
FAQs
1. What makes an expression a polynomial?
A polynomial uses constants and variables with non-negative integer exponents only. It allows addition, subtraction, and multiplication of those terms.
2. Why is 1/x not a polynomial?
The variable sits in the denominator. That makes the exponent effectively negative, which breaks the polynomial rule.
3. Are square roots of variables allowed?
No. A square root means a fractional exponent, and polynomial exponents must be whole numbers starting at zero.
4. Can grouped expressions still be polynomial?
Yes. Expressions like (x+1)^3 are polynomial because the grouped power expands into valid terms with non-negative integer exponents.
5. Does a constant count as a polynomial?
Yes. Any real constant is a polynomial. Its degree is zero in standard reporting.
6. Can a polynomial contain multiple variables?
Yes. Expressions like 3x^2y + 4y^3 are polynomial when every variable keeps non-negative integer exponents.
7. Why does a function like sin(x) fail?
Named functions of variables are not polynomial terms. Polynomial structure only uses powers, constants, and arithmetic combinations.
8. Why did my input return invalid instead?
That usually means the syntax was incomplete or unsupported. Check parentheses, operators, and characters, then try again.