Overview
Simplifying a polynomial means combining like terms, which are terms with the same variable raised to the same power. The result is an equivalent polynomial that is shorter and easier to read and evaluate.
Formula
Add the coefficients for each exponent separately: aₙxⁿ + bₙxⁿ = (aₙ + bₙ)xⁿ.
How it works
Enter the expression
Write the polynomial using x and ^ for exponents.
Identify like terms
Order the terms by exponent from highest to lowest.
Combine coefficients
Add the coefficients for each exponent and keep the exponent unchanged.
Read the result
The simplified form, degree and leading coefficient appear.
Worked examples
Example 1: 3x² + 2x − 5 + x² − 4x + 1
Combines to 4x² − 2x − 4, with degree 2.
Example 2: 5x³ − 2x + 7 − 5x³
Combines to −2x + 7, a first-degree polynomial.
Frequently asked questions
Can I use negative exponents?
No. Polynomials use only nonnegative integer exponents.
What is the constant term?
The term without the variable, that is, the term with exponent zero.
Does term order matter?
The value does not change, but descending order by exponent is the standard form.
This calculator is for educational and informational purposes only and is not a substitute for professional advice.