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 $$(2y^5 + 3y^3 + 2 + 7)$$ How to add, subtract polynomial

Subtracting Polynomials

Example 2

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

$$ (3y^5 - 2y + y^4 + 2y^3 + 5)$$ and $$(2y^5 + 3y^3 + 2 + 7)$$ how to subtract polynomials

Practice Problems

Problem 1

Add the following polynomials: $$(x^3 + 5x + 3x^2 + 2)$$ and $$(4x^3 + 3x^2 + 14)$$

This problem is like example 1.

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

add polynomial
Problem 2

Find the sum of following polynomials: $$ (2x^3 + 5x^4 + 3x^2 + 12)$$ and $$(7x^3+ 4x^2 + 3)$$

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 2b
Problem 3

Subtract following polynomials: $$(3x^2 + 2x^3 + 12x^7 + 12) \red - (4x^2 + 3 - 11x^3)$$

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 3b
Problem 4

Add following polynomials: $$ (2x^8 + 6x^7 + 3x^9)$$ + $$(5x^2 + 4 + 9x^3)$$

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.

problem4b
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