Polynomial Calculator

Add, subtract, multiply, or divide two polynomials. The calculator collects like terms, expands products, and performs polynomial long division with a quotient and remainder — showing each step.

Result —

How to Add, Multiply, and Divide Polynomials

Enter two polynomials, choose an operation, and the calculator shows the result and the working.

1

Add or subtract by combining like terms

Terms with the same power of the variable are added or subtracted together; for subtraction the sign of every term in B is flipped first.

2

Multiply with the distributive property

Every term of A is multiplied by every term of B — the FOIL method for binomials — and the calculator collects the like terms into standard form.

3

Divide to get a quotient and remainder

Long division returns a quotient plus any remainder over the divisor. To break a single polynomial into factors instead, use the Factoring Calculator; to solve ax² + bx + c = 0, use the Quadratic Formula Calculator.

Frequently Asked Questions

How do you add and subtract polynomials?
To add or subtract polynomials you combine like terms — terms with the same variable raised to the same power. Line up the x² terms, the x terms, and the constants, then add or subtract their coefficients. For subtraction, remember to change the sign of every term in the second polynomial before combining. This calculator does the alignment and the arithmetic for you and returns the answer in standard form.
How do you multiply two polynomials?
Multiplying polynomials uses the distributive property: multiply every term of the first polynomial by every term of the second, adding the exponents on matching variables, then collect like terms. For two binomials this is the familiar FOIL method, and the same idea extends to any size. This calculator expands the full product and simplifies it to standard form automatically.
How does polynomial long division work?
Polynomial long division mirrors the long division you use for numbers. You divide the leading term of the dividend by the leading term of the divisor to get the next term of the quotient, multiply the whole divisor by that term, subtract, and bring down the next term — repeating until the remainder has a lower degree than the divisor. The result is a quotient plus a remainder over the divisor. This calculator carries out every step and reports both the quotient and the remainder.
What is the degree of a polynomial?
The degree of a polynomial is the highest power of the variable that appears with a non-zero coefficient. For example, 2x³ − 4x + 1 has degree 3, and a plain constant like 7 has degree 0. The degree tells you how the polynomial behaves and, in division, when to stop: you keep going until the remainder's degree is smaller than the divisor's.

Related algebra calculators

Factoring Calculator

Factor a polynomial over the rationals — GCF, difference of squares, and rational-root steps.

Algebra

→

Quadratic Formula Calculator

Solve ax² + bx + c = 0 for real or complex roots, with the discriminant and every step.

Algebra

→

Slope Calculator

Slope from two points, plus the angle, y = mx + b, distance, and midpoint.

Algebra

→

System of Equations Solver

Solve two linear equations in two unknowns with Cramer's rule, step by step.

Algebra

→

All Math Calculators

Algebra, matrices, statistics and geometry with step-by-step solutions.

Math

→