Adding Polynomials

To add polynomials, remove the parentheses and combine the like terms. When a plus sign comes before the parentheses, every term inside keeps its sign. In 3x^2 + 2x + (x^2 - 5x), removing the parentheses gives 3x^2 + 2x + x^2 - 5x.

Now group the terms by degree and add their coefficients. The squared terms give 3x^2 + x^2 = 4x^2. The x terms give 2x - 5x = -3x. The sum is 4x^2 - 3x.

After removing the parentheses, group the terms that have the same variable and the same exponent. Add their coefficients to get the simplified polynomial. In the example, 3x^2 and x^2 are like terms, and so are 2x and -5x. The terms x^2 and x are not like terms, so they stay separate.