Polynomial Operations

Addition, subtraction and multiplication of polynomials follow the Algebra procedures studied in elementary school.

When we have sums or subtractions it is enough to reduce similar terms, that is, to operate separately powers of the same degree.

In multiplications, we simply apply the distributive property and then reduce the similar terms.

Addition of Polynomials


Polynomial Subtraction


Polynomial Multiplication


If A (x) and B (x) are polynomials, we have to:

  • If A (x) and B (x) have different degrees, the degree of A (x) + B (x) or A (x) - B (x) equals the largest between the degrees of A (x) and B (x).
  • If A (x) and B (x) are of the same degree, the degree of A (x) + B (x) or of A (x) - B (x) may be less than or equal to the degree of polynomials A (x) and B (x) or the resulting polynomial may be null.
  • The degree of A (x) .B (x) is the sum of the degrees of A (x) and B (x).
Next: Polynomial Division