Subjects

Careers

Open the App

Subjects

Easy Steps: How to Factor Polynomials and Solve Problems

Open

25

0

user profile picture

Mira

6/12/2023

Algebra 2

factoring and dividing with polynomials

Easy Steps: How to Factor Polynomials and Solve Problems

This document provides an overview of factoring polynomials and polynomial division techniques. It covers various methods for factoring, including difference of squares, sum or difference of cubes, quadratic factoring, and grouping. The guide also explains polynomial long division and synthetic division.

Overall Summary:

A comprehensive guide on how to factor polynomials and perform polynomial division, covering:

  • Factoring techniques for polynomials with different numbers of terms
  • Polynomial long division
  • Synthetic division
  • Examples and step-by-step solutions for various factoring and division problems
...

6/12/2023

440

Can't find what you're looking for? Explore other subjects.

Knowunity is the # 1 ranked education app in five European countries

Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.

Ranked #1 Education App

Download in

Google Play

Download in

App Store

Knowunity is the # 1 ranked education app in five European countries

4.9+

Average App Rating

21 M

Students use Knowunity

#1

In Education App Charts in 17 Countries

950 K+

Students uploaded study notes

Still not sure? Look at what your fellow peers are saying...

iOS User

I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D

Stefan S, iOS User

The application is very simple and well designed. So far I have found what I was looking for :D

SuSSan, iOS User

Love this App ❤️, I use it basically all the time whenever I'm studying

 

Algebra 2

440

Jun 12, 2023

1 page

Easy Steps: How to Factor Polynomials and Solve Problems

This document provides an overview of factoring polynomials and polynomial division techniques. It covers various methods for factoring, including difference of squares, sum or difference of cubes, quadratic factoring, and grouping. The guide also explains polynomial long division and synthetic... Show more

(
finol study guide
1. factoring:
→ always factor out the gef first, if there is one
a. difference of squares: a²_b² → (a+b) (a-b)
La
FACTOR

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Factoring Techniques

This section covers various methods for factoring polynomials with different numbers of terms, including:

  1. Factoring out the Greatest Common Factor GCFGCF
  2. Difference of Squares
  3. Sum or Difference of Cubes
  4. Factoring Quadratics
  5. Factoring by Grouping
  6. Other Factoring Techniques

Highlight: Always factor out the Greatest Common Factor GCFGCF first, if there is one.

Example: For difference of squares: a² - b² → a+ba+baba-b

Vocabulary: Difference of Squares - A special case of factoring where a polynomial is in the form a² - b².

Example: For sum of cubes: a³ + b³ → a+ba+ba2ab+b2a² - ab + b²

Example: For difference of cubes: a³ - b³ → aba-ba2+ab+b2a² + ab + b²

Highlight: When factoring quadratics ax2+bx+cax² + bx + c, find two factors of ac that add up to b.

Example: Factoring x² + 8x + 12:

  1. Factors of 12 that add up to 8 are 6 and 2
  2. Rewrite as x² + 6x + 2x + 12
  3. Factor by grouping: xx+6x+6 + 2x+6x+6
  4. Final result: x+2x+2x+6x+6

Vocabulary: Factor by Grouping - A method used to factor polynomials with four or more terms by separating them into groups.

Polynomial Long Division

This section explains the process of polynomial long division, which is similar to regular long division but with polynomials.

Highlight: Don't forget to use placeholders for any missing degrees in the polynomial.

Example: Dividing 2x2+x32x² + x - 3 by x+1x + 1:

  1. Divide first terms: 2x² ÷ x = 2x
  2. Multiply: 2xx+1x + 1 = 2x² + 2x
  3. Subtract: 2x² + x - 3 - 2x2+2x2x² + 2x = -x - 3
  4. Repeat the process with -x - 3
  5. Final result: 2x - 1 with a remainder of -2

Synthetic Division

The guide concludes with an explanation of synthetic division, a shortcut method for dividing polynomials.

Vocabulary: Synthetic Division - A simplified method of polynomial long division, particularly useful when dividing by a linear factor.

Example: Synthetic division of 2x⁴ - 7x³ - 7x + 1 by x4x - 4:

  1. Write coefficients: 2 -7 0 -7 1
  2. Use 4 as the divisor rootofx4root of x - 4
  3. Bring down first coefficient: 2
  4. Multiply 2 by 4 and add to -7: 244 + 7-7 = 1
  5. Continue this process for all terms
  6. Final result: 2x³ + x² + 4x + 9 with a remainder of 37

Highlight: Use zero as a placeholder for missing terms in the polynomial during synthetic division.

Can't find what you're looking for? Explore other subjects.

Students love us — and so will you.

4.9/5

App Store

4.8/5

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 it’s very much worth it and you’ll 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 don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve 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 help🤍🤍

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.😋🩷🎀

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 😍😁😲🤑💗✨🎀😮

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 I’ve 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 it’s very much worth it and you’ll 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 don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve 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 help🤍🤍

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.😋🩷🎀

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 😍😁😲🤑💗✨🎀😮

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 I’ve seen! Geometry too!

Paul T

iOS user