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Biology
Chemistry
AP Chemistry
English
AP English Literature
63
โข
Dec 6, 2025
โข
Magali ๐
@magalilyu
Polynomial functions are a fundamental concept in algebra that describe... Show more
Ever wondered what makes a mathematical expression a polynomial? A polynomial is a function expressed as a sum of terms with variables raised to whole number powers. Not everything qualifies though - expressions with negative exponents, variables in denominators, or radicals containing variables are not polynomials.
The general form of a polynomial function looks like:
f(x) = anx^n + an-1x^n-1 + ... + a1x + a0
where n is the degree (highest exponent) and the a-values are coefficients.
Polynomials come in different forms based on their number of terms:
Quick Tip: You can quickly identify polynomial types by counting their terms, and their degree by finding the highest exponent on any variable.
The degree also tells us what type of function we're dealing with. Linear functions (degree 1) create straight lines, while quadratic functions (degree 2) form parabolas when graphed.
Cubic functions (polynomials with degree 3) create S-shaped curves with interesting features. When graphing any polynomial, look for relative minimums (valleys where the function changes from decreasing to increasing) and relative maximums (peaks where the function changes from increasing to decreasing).
Two important theorems govern polynomial behavior. The Factor Theorem states that a polynomial f(x) has a factor if and only if f(k)=0. This helps us find zeros of polynomials, which are the x-values that make the function equal zero.
The Fundamental Theorem of Algebra guarantees that a polynomial of degree n will have exactly n roots (though some may be complex or repeated). The behavior at these zeros depends on their multiplicity:
Remember This: The end behavior of a polynomial (how it acts as x approaches positive or negative infinity) depends on its degree and leading coefficient. Even-degree polynomials have matching end behaviors, while odd-degree polynomials have opposite end behaviors.
Understanding these patterns makes sketching polynomial graphs much easier - you can predict how the function will behave without plotting every point.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think itโs very much worth it and youโll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still donโt get it!!! In the end I think itโs worth it ๐๐ โ ๏ธAlso DID I MENTION ITS FREEE YOU DONโT HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLYโ๏ธโ๏ธโ ๏ธ
Thomas R
iOS user
Knowunity is the BEST app Iโve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help๐ค๐ค
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.๐๐ฉท๐
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as Iโve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think itโs very much worth it and youโll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still donโt get it!!! In the end I think itโs worth it ๐๐ โ ๏ธAlso DID I MENTION ITS FREEE YOU DONโT HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLYโ๏ธโ๏ธโ ๏ธ
Thomas R
iOS user
Knowunity is the BEST app Iโve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help๐ค๐ค
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.๐๐ฉท๐
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as Iโve seen! Geometry too!
Paul T
iOS user
Magali ๐
@magalilyu
Polynomial functions are a fundamental concept in algebra that describe expressions with variables raised to non-negative integer powers. Understanding polynomials helps you work with a wide range of mathematical models and is essential for success in algebra and higher math... Show more
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Ever wondered what makes a mathematical expression a polynomial? A polynomial is a function expressed as a sum of terms with variables raised to whole number powers. Not everything qualifies though - expressions with negative exponents, variables in denominators, or radicals containing variables are not polynomials.
The general form of a polynomial function looks like:
f(x) = anx^n + an-1x^n-1 + ... + a1x + a0
where n is the degree (highest exponent) and the a-values are coefficients.
Polynomials come in different forms based on their number of terms:
Quick Tip: You can quickly identify polynomial types by counting their terms, and their degree by finding the highest exponent on any variable.
The degree also tells us what type of function we're dealing with. Linear functions (degree 1) create straight lines, while quadratic functions (degree 2) form parabolas when graphed.
Access to all documents
Improve your grades
Join milions of students
By signing up you accept Terms of Service and Privacy Policy
Cubic functions (polynomials with degree 3) create S-shaped curves with interesting features. When graphing any polynomial, look for relative minimums (valleys where the function changes from decreasing to increasing) and relative maximums (peaks where the function changes from increasing to decreasing).
Two important theorems govern polynomial behavior. The Factor Theorem states that a polynomial f(x) has a factor if and only if f(k)=0. This helps us find zeros of polynomials, which are the x-values that make the function equal zero.
The Fundamental Theorem of Algebra guarantees that a polynomial of degree n will have exactly n roots (though some may be complex or repeated). The behavior at these zeros depends on their multiplicity:
Remember This: The end behavior of a polynomial (how it acts as x approaches positive or negative infinity) depends on its degree and leading coefficient. Even-degree polynomials have matching end behaviors, while odd-degree polynomials have opposite end behaviors.
Understanding these patterns makes sketching polynomial graphs much easier - you can predict how the function will behave without plotting every point.
Our AI companion is specifically built for the needs of students. Based on the millions of content pieces we have on the platform we can provide truly meaningful and relevant answers to students. But its not only about answers, the companion is even more about guiding students through their daily learning challenges, with personalised study plans, quizzes or content pieces in the chat and 100% personalisation based on the students skills and developments.
You can download the app in the Google Play Store and in the Apple App Store.
That's right! Enjoy free access to study content, connect with fellow students, and get instant help โ all at your fingertips.
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Transform this note into: โ 50+ Practice Questions โ Interactive Flashcards โ Full Mock Exam โ Essay Outlines
App Store
Google Play
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think itโs very much worth it and youโll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still donโt get it!!! In the end I think itโs worth it ๐๐ โ ๏ธAlso DID I MENTION ITS FREEE YOU DONโT HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLYโ๏ธโ๏ธโ ๏ธ
Thomas R
iOS user
Knowunity is the BEST app Iโve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help๐ค๐ค
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.๐๐ฉท๐
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as Iโve seen! Geometry too!
Paul T
iOS user
The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.
Stefan S
iOS user
This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.
Samantha Klich
Android user
Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.
Anna
iOS user
I think itโs very much worth it and youโll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still donโt get it!!! In the end I think itโs worth it ๐๐ โ ๏ธAlso DID I MENTION ITS FREEE YOU DONโT HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLYโ๏ธโ๏ธโ ๏ธ
Thomas R
iOS user
Knowunity is the BEST app Iโve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades
Brad T
Android user
Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help๐ค๐ค
David K
iOS user
The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!
Sudenaz Ocak
Android user
In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.
Greenlight Bonnie
Android user
I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend
Aubrey
iOS user
Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.๐๐ฉท๐
Marco B
iOS user
THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH ๐๐๐ฒ๐ค๐โจ๐๐ฎ
Elisha
iOS user
This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as Iโve seen! Geometry too!
Paul T
iOS user
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