Subtracting polynomials


Before, you start this lesson about subtracting polynomials, make sure you have mastered addition of polynomials

Furthermore, you have to understand how to add and subtract integers

There is no way around these or you will struggle!

Example #1:


Subtract 2x2 + -3x + 4 from 3x2 + 5x + 8

Step #1:

Rewrite the problem

3x2 + 5x + 8 − (2x2 + -3x + 4)

Replace minus sign by + -

3x2 + 5x + 8 + -(2x2 + -3x + 4)

The negative sign will change the sign for every term inside the parenthesis. It is just like taking the opposite

Therefore if something is positive, it will become negative. If it is negative, it will become positive

3x2 + 5x + 8 + -(2x2 + -3x + 4) = 3x2 + 5x + 8 + -2x2 + 3x + -4

Combine all like terms. You could use parenthesis to keep things organized

3x2 + 5x + 8 + -2x2 + 3x + -4     = (3x2 + -2x2 ) + (5x + 3x) + 8 + -4

                                                 = (3 + -2) x2 + (5 + 3)x + 4

                                                 = 1x2 + (8)x + 4

                                                 = x2 + 8x + 4

Example #2:


Subtract 4x2 + 6x + 5 from -8x2 + -4x + 8

Step #1:

Rewrite the problem

-8x2 + -4x + 8 − (4x2 + 6x + 5)

Replace minus sign by + -

-8x2 + -4x + 8 + -(4x2 + 6x + 5)



The negative sign will change the sign for every term inside the parenthesis. It is just like taking the opposite

Therefore, if something is positive, it will become negative. If it is negative, it will become positive

-8x2 + -4x + 8 + -(4x2 + 6x + 5) = -8x2 + -4x + 8 + -4x2 + -6x + -5

Combine all like terms. You could use parenthesis to keep things organized

-8x2 + -4x + 8 + -4x2 + -6x + -5 = (-8x2 + -4x2 ) + (-4x + -6x) + 8 + -5

                                                 = (-8 + -4) x2 + (-4 + 6)x + 3

                                                 = (-12)x2 + (-10)x + 3

                                                 = -12x2 + -10x + 3


I did not use algebra tiles for this lesson about subtracting polynomials.

Any problems, use the form here to send your questions





Recent Articles

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

            Follow me on Pinterest





Recent Lessons

  1. How to estimate fractions

    Dec 11, 17 08:45 AM

    Learn how to estimate fractions with this easy to follow lesson.

    Read More

  Our Top Pages

Formula for percentage

Compatible numbers

Basic math test

Basic math formulas

Types of angles

Math problem solver

Algebra word problems

Surface area of a cube

Finding the average 

Scale drawings

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!


Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests. 


Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.

 Recommended

Scientific Notation Quiz

Types of Angles Quiz

Graphing Slope Quiz

Adding and Subtracting Matrices Quiz  

Factoring Trinomials Quiz 

Solving Absolute Value Equations Quiz  

Order of Operations Quiz