How to Add and Subtract Polynomials

Step By Step

Whether you want to add polynomials or subtract them, you follow a similar set of steps.

General Steps

Step 1

Arrange 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 2

Arrange the like terms in columns and add the like terms.

Example 1

Let's find the sum of the following two polynomials.

$$(3y^5 - 2y + y^4 + 2y^3 + 5)$$ and $$(2y^5 + 3y^3 + 2 + 7)$$

Subtracting Polynomials

Example 2

Let's find the difference of the same two polynomials.

$$(3y^5 - 2y + y^4 + 2y^3 + 5)$$ and $$(2y^5 + 3y^3 + 2 + 7)$$

Practice Problems

Problem 1

This problem is like example 1.

First, remember to rewrite each polynomial in standard form, line up the columns and add the like terms.

Problem 2

This problem is like example 1.

First, remember to rewrite each polynomial in standard form, line up the columns and add the like terms.

Problem 3

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 $$-11x^3$$ term; it is already negative, so subtracting a negative leads to a positive $$11x^3$$)
Problem 4

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.