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.