adding polynomials

Adding polynomials is like sorting laundry: you put the socks with the socks and the shirts with the shirts. The x^2 terms join the x^2 terms, the x terms join the x terms, and the plain numbers join each other. These matched-up pieces are called like terms.

Concretely, to add two polynomials you drop the parentheses, then combine like terms by adding their coefficients while keeping the variable part unchanged. For (3x^2 + 2x) + (x^2 - 5x), the x^2 terms give 4x^2 and the x terms give -3x, so the answer is 4x^2 - 3x.

Subtracting is the same idea with one extra care: distribute the minus sign to every term inside the second polynomial first, flipping each sign, and then add. The single most common mistake is forgetting to flip the sign of every term after the first one.