Polynomial Simplifier Calculator

Calculator Input

Polynomial Expression

Variable Letter

Use one letter only, such as x, y, or z.

Supported Operations

+ addition

- subtraction

* multiplication

^ integer powers and parentheses

Example Data Table

#	Input Expression	Simplified Output	Degree
1	3x^2 + 4x - 7 + 2x^2 - x + 9	5x^2 + 3x + 2	2
2	(x + 2)(x + 3) - x	x^2 + 4x + 6	2
3	(2x - 1)^2 + x - 5	4x^2 - 3x - 4	2
4	5y^3 - 2y + y^3 + 7	6y^3 - 2y + 7	3

Formula Used

Polynomial simplification combines like terms after expanding supported operations. Like terms share the same variable and exponent, so only their coefficients change.

a·xⁿ + b·xⁿ = (a + b)·xⁿ

(a·x^m)(b·xⁿ) = (ab)·x^m+n

(P(x))^k = P(x) × P(x) × ... × P(x), for non-negative integers k

The calculator tokenizes the expression, handles parentheses and powers, expands the polynomial, then merges every matching exponent into one simplified term.

How to Use This Calculator

Enter the polynomial expression using one variable only.
Use +, -, *, parentheses, and integer powers where needed.
If multiplication is implied, you may type forms like 3x or (x+1)(x-2).
Choose the variable letter matching your expression.
Press Simplify Polynomial to display the result above the form.
Download the resulting combined terms as CSV or PDF for notes, homework, or checking.

Frequently Asked Questions

1. What does this calculator simplify?

It simplifies single-variable polynomial expressions by combining like terms, expanding multiplication, applying parentheses, and evaluating non-negative integer exponents.

2. Can it handle implicit multiplication?

Yes. Entries such as 3x, 2(x+1), or (x+2)(x-4) are recognized and internally converted into explicit multiplication before simplification.

3. Does it support variables other than x?

Yes. You may choose one variable letter, such as y or z, and the calculator will simplify the polynomial using that variable consistently.

4. Are decimal coefficients allowed?

Yes. Decimal numbers are accepted in coefficients and constant terms, which is useful for practice problems, modelling, and classwork checks.

5. Can it simplify expressions with division?

No. This version focuses on polynomial addition, subtraction, multiplication, parentheses, and integer exponents. Rational-expression division is not included here.

6. Why does the result show degree and leading coefficient?

These values summarize the simplified polynomial quickly. They help verify structure, compare answers, and understand the highest-order behavior of the expression.

7. What if my expression returns an error?

Check for unsupported symbols, mismatched parentheses, repeated decimal points, or non-integer exponents. Correcting the input format usually resolves the issue.

8. What do the CSV and PDF exports include?

They include the simplified polynomial summary and the combined like-terms table, making it easier to save results for reports, lessons, or revision.