Whether you want to add polynomials or subtract them, you follow a similar set of steps.
Adding Polynomials
Step 1Arrange the Polynomial in standard form
Standard form of a polynomial just means that the term with highest degree is first and each of the following terms
Step 2Arrange the like terms in columns and add the like terms
Example 1
Let's find the sum of the following two polynomials
(3y5 − 2y + y4 + 2y3 + 5) and (2y5 + 3y3 + 2+ 7)
Subtracting Polynomials
Example 2
Let's find the difference of the same two polynomials
(3y5 − 2y + y4 + 2y3 + 5) and (2y5 + 3y3 + 2+ 7)
Practice Problems
This problem is like example 1.
First, remember to rewrite each polynomial in standard form, line up the columns and add the like terms.
This problem is like example 1
First, remember to rewrite each polynomial in standard form, line up the columns and add the like terms.
This problem is like example 2 since we are subtracting.
First, remember to rewrite each polynomial in standard form, line up the columns and add the like terms.
(Be careful with -11x3 term, since it is already negative, when you subtract the term becomes positive as you can see in the work below.)
Although this problem involves addition, there are no like terms. If you line up the polynomials in columns, you will see that no terms are in the same columns.
