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.


Adding Polynomials

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

(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) how to subtract polynomials

Practice Problems

Problem 1

Add the following polynomials: (x3+ 5x + 3x2 +2) and (4x3 + 3x2+ 14)

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

Find the sum of following polynomials: (2x3+ 5x4 + 3x2 +12) and (7x3 + 4x2+ 3)

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

Subtract following polynomials: (3x2+ 2x3+ 12x7 + 12) - ( 4x2+ 3 - 11x3 )

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.)
Problem 4

Add following polynomials: (2x8 + 6x7+ 3x9 + 5) + ( 5x2 + 4 + 9x3 )

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.

Polynomials Home Multiply Polynomial by Monomial