Adding (or subtracting) polynomials is really just an exercise in collecting like terms. For example, if we want to add the polynomial
2x2 + 4x – 3
to the polynomial
6x – 4,
we would just put them together and collect like terms:
Notice that the parentheses in the first line are only there to distinguish the two polynomials.
Although this is basically just a bookkeeping activity, it can get a little messy when there are many terms. One way to help keep things straight is use the column format for addition, keeping like terms lined up in columns:
This method is particularly helpful in the case of subtraction, because it is too easy to make a mistake distributing the minus sign when you write it all in one row.