How to Add and Subtract Polynomials

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)

Problem 1 ) Add the following polynomials:

(x³+ 5x + 3x² +2) and (4x³ + 3x²+ 14)

Step 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.

Step 2

Problem 2 ) Find the sum of following polynomials:

(2x³+ 5x⁴ + 3x² +12) and (7x³ + 4x²+ 3)

Step 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.

Step 2

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Problem 3 ) Subtract following polynomials:

(3x²+ 2x³+ 12x⁷ + 12) - ( 4x²+ 3 - 11x³ )

Step 1

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.

Step 2

( 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 )

Step 1

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.

Step 2