Add Polynomials

Adding Polynomials

Adding polynomials means combining terms that have the same variable part. A like term has the same variables raised to the same powers, such as (3x^2) and (-5x^2). Terms with different powers or different variables cannot be combined.

Method

1. Remove parentheses if they are present. If a polynomial is being added, keep the signs of every term inside each group.
2. Group like terms: constants with constants, (x)-terms with (x)-terms, (x^2)-terms with (x^2)-terms, and so on.
3. Add the coefficients of each group.
4. Write the simplified polynomial in descending order of powers when possible.

Example idea

If you have ((2x^2 + 3x - 1) + (5x^2 - x + 4)), combine the matching parts:

• (2x^2 + 5x^2 = 7x^2)
• (3x - x = 2x)
• (-1 + 4 = 3) So the result is (7x^2 + 2x + 3).

Check your work

Make sure every term from the original expressions appears in the final answer and that only like terms were combined. A quick check is to scan term by term and confirm no power was changed during addition.