ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel


Updated on June 15, 2013


In Algebra, Polynomials are commonly used as lessons, and you might see them more than once. I have been learning all about polynomials for awhile now, and in my eyes, they are easy and fun. However, this may not be the case for everyone, so I want to give everyone a chance to have fun with polynomials and excel in them. I love polynomials, and I hope you do too.

Types of Polynomials

There are many polynomials, and here they are!

Monomial-1 term

Binomial- 2 terms

Trinomial- 3 terms

Mono- is the Latin root for 1

Bi- is the Latin root for 2

Tri- is the Latin root for 3

5x is a monomial

2x+5 is a binomial

x squared+x+5 is a trinomial

Please Read

I can't do the small 2 for squared on this lens, so I just write out the word squared instead.

Adding Polynomials

One of the first steps to polynomials is learning how to add and subtract them. You can only add and subtract like terms. Let's take a look at the first example.

2x squared-5x+17

+5x squared+8


This is a tricky one. 2x squared and 5x squared definitely add up to 7 x squared. However, you must also know that you cannot add -5x and 8 together because they are not like terms. You can add 17 and 8 together because they are like terms. If you have a problem remembering this, you can put 0x under -5x (0x can be plus or minus because it does not affect the equation, it's just a place holder). Then the equation would look like this:

2x squared-5x+17

+5x squared-0x+8


7x squared-5x+25

Was that easier? You have to see that sometimes, a polynomial will be out of place. Your teachers will try to trick newbies with this method so that they can learn from their mistakes. That is why the placeholder trick can help out.

Subtracting Polynomials

Subtracting Polynomials can be converted to addition, which would make things a lot easier. Subtracting Polynomials is like adding their opposites, and that is the best approach to solving them. Let's look at one example.

2x squared+6x-8

-3x squared+7x-8


You can change the minus sign to a plus sign, and then switch everything else. Remember that 3x squared is positive, but the minus sign is in front. This is what the new equation would look like. THE TOP REMAINS THE SAME

2x squared+6x-8

+ -3x squared-7x+8


Now, isn't that easier? 2x squared plus negative 3x squared is negative x squared. 6x plus a negative 7x equals -x, and -8+8=0.

This is the final answer.

2x squared+6x-8

+ -3x squared-7x+8


-x squared-x+0

Negative x squared minus x plus 0.

For beginners, I recommend adding the 0 so that you know it's there, but as you learn about polynomials for a long time, you should take out the 0.

Multiplying Polynomials Part 1


FOIL is the term that is used to help out when we have to multiply two binomials.





You can think of FOIL as a Punnett Square, and the picture perfectly describes one way that you can approach FOIL.

Let's look at the example in the Punnett Square.

(x+3) (x+6)

This is what it would look like:

(x times x)+(x times 6)+(3 times x)+(3 times 6)


Your final answer is this:

x squared+9x+18.

TIP: When the value of both x's is 1, you will always get x squared, and if you add the two constants together (numbers without variables such as 3 and 6) and get the x value. So, in (x+6) (x+3), just do 3+6 and put the x at the end of the number. That is how we got 9x for the x term. You cannot use this method if x>1.

So, in (2x+5) (3x+6), you will have to do some more math to find the answer.

So, with the method of FOIL, the answer was.....

6x squared+27x+30. FOIL will help you solve the multiplication of two binomials.

Squaring a Binomial

If you EVER see (x+1) squared, then it means (x+1) (x+1). Writing it out will prevent you from forgetting the middle term which in this sample would be 2x.

Dividing A Trinomial

When you divide a trinomial by a binomial, 99% of the time, that binomial is a factor of the trinomial. Let's take a look at an example:

(2x squared+5x+2)



The 2x+1 is a factor of the trinomial.

(2x+1) ???



Now, we have to find out what the ??? stands for. The two constants must have a product of 2, and you must have a middle term of 5x. Also, you must have 2x squared. Since you already have 2x, all you need now is x. Then, through testing out the factors of 2, you will realize that 2 is the constant. So, now the equation looks like this:

(2x+1) (x+2)



The 2x+1's cancel out leaving you with (x+2). You can check the binomials first through FOIL, but they will bring you back to 2x squared+5x+2.

Awesome Books About Polynomials

Look Out For This One!

There is one thing that you must be aware of when you are solving these kinds of polynomials. Let's look at the example below.

(x+2) squared

The most common mistake most people make is squaring what is in the parenthesis to get an answer of x squared+4. This is incorrect because you multiply the polynomial by the same polynomial. Look at the example below.

(x+2) squared

(x+2) (x+2)

So, now you know what it means to square the number. It may look the same as x squared+4, but when you write out the entire polynomial, you will realize that there IS a middle term. Look out for this one.

Bugs Bunny isn't Daffy Duck and Daffy Duck isn't Bugs Bunny.

How Do You Like A Polynomials? - Did I Do A Good Job?

    0 of 8192 characters used
    Post Comment

    • theholidayplace profile image


      6 years ago

      very interesting, great to know that some many practical problems can be solve with the use of polynomials


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at:

    Show Details
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the or domains, for performance and efficiency reasons. (Privacy Policy)
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)