Polynomial Calculator

Add, subtract, and multiply polynomials. Enter two polynomials and select an operation to see step-by-step solutions.

Polynomial Operations

Enter coefficients as comma-separated values (highest power to constant term)

Polynomial Operations

Adding Polynomials

Add coefficients of like terms (same degree):

(2x² + 3x + 1) + (x² - 2x + 4) = 3x² + x + 5

Subtracting Polynomials

Subtract coefficients of like terms (same degree):

(2x² + 3x + 1) - (x² - 2x + 4) = x² + 5x - 3

Multiplying Polynomials

Multiply each term of the first polynomial by each term of the second:

(x + 2)(x + 3) = x² + 5x + 6

The FOIL method for binomials:

  • First: Multiply first terms
  • Outer: Multiply outer terms
  • Inner: Multiply inner terms
  • Last: Multiply last terms

Examples

Example 1: Addition

Add: (2x² + 3x - 1) + (x + 4)

Align like terms

2x² + (3x + x) + (-1 + 4)

2x² + 4x + 3

Example 2: Subtraction

Subtract: (x² + 5x + 6) - (x + 2)

Distribute negative sign

x² + 5x + 6 - x - 2

x² + 4x + 4

Example 3: Multiplication

Multiply: (x + 2)(x + 3)

FOIL: x² + 3x + 2x + 6

x² + 5x + 6

Example 4: Multiply Quadratics

Multiply: (x² + 1)(x² - 1)

Difference of squares

x⁴ - 1

Example 5: Multiply Higher Degree

Multiply: (2x + 1)(3x² - 2x + 4)

Distribute: 6x³ - 4x² + 8x + 3x² - 2x + 4

6x³ - x² + 6x + 4