Adding and Subtracting Polynomials

Polynomials can only be added or subtracted when both the variable and its power are the same. If either of them is different then the two terms cannot be added or subtracted. If they are the same then you add or subtract the two term’s coefficients together, the variable and its power are unchanged.

Take the following expression:

Polynomial - 3.png

To see if we can simplify this expression we first check to see what the variables each term has. In this case, all of the terms have the same variablex. Next, we have to check the powers associated with each of variables. The first two terms have powers of 2, and the third terms have a power of 3. So, we can only add the first two terms together because they have the same variable and power, but not the third term because it has a different power.

To add the first two terms together, we add the two coefficients together. The two coefficients are and 2 and adding them together gives us a 5. So, the simplified expression is:

Polynomial - 4.png

Note, that even though we added the first two terms together the variable and its power is unchanged. The only thing that changed was that the coefficients were added together.