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Greatest Common Factor

Greatest Common Factor

187

•

Jan 26, 2023

•

3 pages

Solving Quadratics by Factoring: Easy Steps and Fun Worksheets

user profile picture

Bill

@bill_uidw

The X-method is a powerful technique for factoring quadratic equations... Show more

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

Factor Quadratics - Day 2

This section focuses on more advanced factoring techniques, combining the Greatest Common Factor GCFGCF method with the X-method.

The process involves two main steps:

  1. Factor out the GCF if possible.
  2. Use the X-method to factor the remaining quadratic expression.

Example: For 5m² - 10m - 15, first factor out the GCF of 5: 5m2−2m−3m² - 2m - 3. Then use the X-method on m2−2m−3m² - 2m - 3 to get 5m+1m+1m−3m-3.

Several practice problems are provided, including:

  • 24n² + 16n - 48
  • 5m² + 5m - 100
  • 28k² + 28k

Highlight: Remember to always check for a GCF before applying the X-method when solving quadratic equations by factoring.

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

Solve Quadratics by Factoring (GCF, X-method)

This page outlines the complete process for solving quadratic equations by factoring, combining all the techniques learned.

The steps for solving are:

  1. Make the equation equal to zero addtheoppositeifnecessaryadd the opposite if necessary.
  2. Factor out the GCF, if possible.
  3. Use the X-method to factor further, if possible.
  4. Set each factor to zero and solve for x.

Vocabulary: The solutions to a quadratic equation are also called roots, zeros, or x-intercepts.

Example: For x² - 10x + 16 = 0, we factor to get x−2x-2x−8x-8 = 0, leading to solutions x = 2 or x = 8.

The guide provides several practice problems with detailed solutions, including:

  • 3x² + 25n + 20 = 0
  • x² + 16x + 60 = 0
  • 2x² + 13x + 42 = 0

Highlight: When solving quadratic equations, always remember to set the equation to zero before factoring.

This comprehensive guide provides students with the tools and practice needed to master solving quadratic equations by factoring.

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

Factor Quadratics: X-method

The X-method is a powerful technique for factoring quadratic equations. This method involves finding two numbers that multiply to give a·c and add to give b in the standard form ax² + bx + c.

Definition: The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

To use the X-method:

  1. Identify the values of a, b, and c in the quadratic expression.
  2. Find two numbers that multiply to give a·c and add to give b.
  3. Rewrite the middle term using these two numbers.
  4. Factor by grouping.

Example: For x² + 16x + 60, we have a=1, b=16, and c=60. The factors of 60 that add up to 16 are 6 and 10. So, the factored form is x+6x+6x+10x+10.

The guide also introduces the concept of converting between standard form and intercept form of quadratic equations.

Vocabulary: Intercept form of a quadratic equation is ax−px-px−qx-q, where p and q are the x-intercepts.

Highlight: Practice problems are provided, including 3x² - 9x - 10 and 3x² + 14x - 80, to help students master the X-method.


Based on the X-method examples, what is the factored form of the quadratic expression 3x² + 14x - 80?

(3x+10)(x-8)

(3x-8)(x+10)

(3x-10)(x+8)

(3x+8)(x-10)


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

Subjects

Arithmetic

Greatest Common Factor

Greatest Common Factor

 

Arithmetic

•

187

•

Jan 26, 2023

•

3 pages

Solving Quadratics by Factoring: Easy Steps and Fun Worksheets

user profile picture

Bill

@bill_uidw

The X-method is a powerful technique for factoring quadratic equations. This method helps students solve quadratic expressions efficiently by finding two numbers that multiply to give the product of the coefficient of x² and the constant term, while also... Show more

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

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

Factor Quadratics - Day 2

This section focuses on more advanced factoring techniques, combining the Greatest Common Factor GCFGCF method with the X-method.

The process involves two main steps:

  1. Factor out the GCF if possible.
  2. Use the X-method to factor the remaining quadratic expression.

Example: For 5m² - 10m - 15, first factor out the GCF of 5: 5m2−2m−3m² - 2m - 3. Then use the X-method on m2−2m−3m² - 2m - 3 to get 5m+1m+1m−3m-3.

Several practice problems are provided, including:

  • 24n² + 16n - 48
  • 5m² + 5m - 100
  • 28k² + 28k

Highlight: Remember to always check for a GCF before applying the X-method when solving quadratic equations by factoring.

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

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

Solve Quadratics by Factoring (GCF, X-method)

This page outlines the complete process for solving quadratic equations by factoring, combining all the techniques learned.

The steps for solving are:

  1. Make the equation equal to zero addtheoppositeifnecessaryadd the opposite if necessary.
  2. Factor out the GCF, if possible.
  3. Use the X-method to factor further, if possible.
  4. Set each factor to zero and solve for x.

Vocabulary: The solutions to a quadratic equation are also called roots, zeros, or x-intercepts.

Example: For x² - 10x + 16 = 0, we factor to get x−2x-2x−8x-8 = 0, leading to solutions x = 2 or x = 8.

The guide provides several practice problems with detailed solutions, including:

  • 3x² + 25n + 20 = 0
  • x² + 16x + 60 = 0
  • 2x² + 13x + 42 = 0

Highlight: When solving quadratic equations, always remember to set the equation to zero before factoring.

This comprehensive guide provides students with the tools and practice needed to master solving quadratic equations by factoring.

<h2 id="factorquadraticsxmethod">Factor Quadratics: X-method</h2> <p>One way to solve quadratic equations is by factoring. There are differ

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

Factor Quadratics: X-method

The X-method is a powerful technique for factoring quadratic equations. This method involves finding two numbers that multiply to give a·c and add to give b in the standard form ax² + bx + c.

Definition: The standard form of a quadratic equation is ax² + bx + c, where a, b, and c are constants and a ≠ 0.

To use the X-method:

  1. Identify the values of a, b, and c in the quadratic expression.
  2. Find two numbers that multiply to give a·c and add to give b.
  3. Rewrite the middle term using these two numbers.
  4. Factor by grouping.

Example: For x² + 16x + 60, we have a=1, b=16, and c=60. The factors of 60 that add up to 16 are 6 and 10. So, the factored form is x+6x+6x+10x+10.

The guide also introduces the concept of converting between standard form and intercept form of quadratic equations.

Vocabulary: Intercept form of a quadratic equation is ax−px-px−qx-q, where p and q are the x-intercepts.

Highlight: Practice problems are provided, including 3x² - 9x - 10 and 3x² + 14x - 80, to help students master the X-method.

According to the transcript, what is the purpose of using the X-method when factoring quadratics?

The X-method helps find two numbers that multiply to equal a*c and add up to equal b in a quadratic equation.

The X-method is used to simplify complex fractions by cross-multiplication.

The X-method is a method for finding the greatest common factor (GCF) of two numbers.

The X-method is a graphical technique for solving systems of linear equations.

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