•

Feb 12, 2026

•

4 pages

Step by Step Synthetic Division Tutorial: Easy Guide with Examples and Answers

George Yassa

@georgeyassa_gqtt

Synthetic division is a step-by-step methodfor dividing polynomials by... Show more

1 / 4

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Long Division Example with Monic Linear Divisor

This page demonstrates the process of long division for polynomials using a monic linear divisor, highlighting the steps involved and introducing the concept of synthetic division.

D. Long Division Example

The page shows a detailed example of dividing 2x³ - 4x² + 7x - 11 by x + 2 using traditional long division.

Example: 2x³ - 4x² + 7x - 11 ÷ $x + 2$ = 2x² - 8x + 23 + 26/ $x + 2$

The process is then simplified by focusing only on the coefficients and changing the divisor to "-2" to facilitate addition instead of subtraction.

Highlight: This simplification process is a step towards synthetic division, which further streamlines the calculation.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Synthetic Division

This page introduces the concept of synthetic division as a shortcut method for dividing polynomials by monic linear divisors.

E. Synthetic Division Process

The page demonstrates how to perform synthetic division using the same example from the previous page: 2x³ - 4x² + 7x - 11 ÷ $x + 2$ .

Definition: Synthetic division is a simplified method for dividing polynomials by monic linear divisors of the form x - c.

Example: Dividing 2x³ - 4x² + 7x - 11 by x + 2 using synthetic division: -2) 2 -4 7 -11 -4 16 -46 2 -8 23 -57 Answer: 2x² - 8x + 23 + 26/ $x + 2$

Highlight: Synthetic division only works for monic linear divisors. For all other cases, algebraic long division must be used.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Examples of Synthetic Division

This page provides two examples of synthetic division to reinforce understanding of the technique.

F. Examples

Example 1: Divide 3x³ - x + 5 by x - 1 using synthetic division

Example:

3 0 -1 5 3 3 2 3 3 2 7 Answer: 3x² + 3x + 2 + 7/ $x - 1$

Example 2: Divide 2x³ + 6x² + 5x - 3 by x + 3 using synthetic division

Example: -3) 2 6 5 -3 -6 0 -15 2 0 5 -18 Answer: 2x² + 5 - 18/ $x + 3$

These examples demonstrate the efficiency of synthetic division compared to traditional long division methods for polynomials.

Highlight: Synthetic division is a powerful tool for quickly dividing polynomials by linear factors, making it invaluable for solving polynomial equations and finding roots.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

3.3B Synthetic Division

This section introduces the concept of synthetic division, a simplified method for dividing polynomials by linear factors. It begins by defining key terms and progresses to demonstrate the technique through examples.

A. Linear Polynomials

Linear polynomials are defined as polynomials of the form ax + b, where a ≠ 0.

Example: 3x - 1, 2x - 5, and 3x - 1 are linear polynomials.

B. Monic Polynomials

Monic polynomials are polynomials with a leading coefficient of 1.

Example: x³ + 5x² - 2x - 1, x² - 3x² - 2, and x + b are monic polynomials.

C. Monic Linear Polynomials

Monic linear polynomials are both linear and monic, taking the form x - c.

Example: x + 5, x - 2, and x + 3 are monic linear polynomials.

Highlight: All monic linear polynomials can be written as x - c, where c can be positive, negative, or zero.

We thought you’d never ask...

What is the Knowunity AI companion?

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.

Where can I download the Knowunity app?

You can download the app in the Google Play Store and in the Apple App Store.

Is Knowunity really free of charge?

That's right! Enjoy free access to study content, connect with fellow students, and get instant help – all at your fingertips.

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

Students love us — and so will you.

4.6/5

App Store

4.7/5

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 Knowunity AI. 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

Stefan S

iOS user

Samantha Klich

Android user

Anna

iOS user

Thomas R

iOS user

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

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

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

Elisha

iOS user

Paul T

iOS user

Algebra 2

•

Feb 12, 2026

•

4 pages

Step by Step Synthetic Division Tutorial: Easy Guide with Examples and Answers

George Yassa

@georgeyassa_gqtt

Synthetic division is a step-by-step methodfor dividing polynomials by linear factors. This technique simplifies the process of polynomial long division, especially when dealing with monic linear divisors. The transcript provides a comprehensive overview of synthetic division, including its definition,... Show more

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Long Division Example with Monic Linear Divisor

This page demonstrates the process of long division for polynomials using a monic linear divisor, highlighting the steps involved and introducing the concept of synthetic division.

D. Long Division Example

The page shows a detailed example of dividing 2x³ - 4x² + 7x - 11 by x + 2 using traditional long division.

Example: 2x³ - 4x² + 7x - 11 ÷ $x + 2$ = 2x² - 8x + 23 + 26/ $x + 2$

The process is then simplified by focusing only on the coefficients and changing the divisor to "-2" to facilitate addition instead of subtraction.

Highlight: This simplification process is a step towards synthetic division, which further streamlines the calculation.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Synthetic Division

This page introduces the concept of synthetic division as a shortcut method for dividing polynomials by monic linear divisors.

E. Synthetic Division Process

The page demonstrates how to perform synthetic division using the same example from the previous page: 2x³ - 4x² + 7x - 11 ÷ $x + 2$ .

Definition: Synthetic division is a simplified method for dividing polynomials by monic linear divisors of the form x - c.

Example: Dividing 2x³ - 4x² + 7x - 11 by x + 2 using synthetic division: -2) 2 -4 7 -11 -4 16 -46 2 -8 23 -57 Answer: 2x² - 8x + 23 + 26/ $x + 2$

Highlight: Synthetic division only works for monic linear divisors. For all other cases, algebraic long division must be used.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

Examples of Synthetic Division

This page provides two examples of synthetic division to reinforce understanding of the technique.

F. Examples

Example 1: Divide 3x³ - x + 5 by x - 1 using synthetic division

Example:

3 0 -1 5 3 3 2 3 3 2 7 Answer: 3x² + 3x + 2 + 7/ $x - 1$

Example 2: Divide 2x³ + 6x² + 5x - 3 by x + 3 using synthetic division

Example: -3) 2 6 5 -3 -6 0 -15 2 0 5 -18 Answer: 2x² + 5 - 18/ $x + 3$

These examples demonstrate the efficiency of synthetic division compared to traditional long division methods for polynomials.

Highlight: Synthetic division is a powerful tool for quickly dividing polynomials by linear factors, making it invaluable for solving polynomial equations and finding roots.

$3.3B Synthetic Division A. Linear Polynomials A linear polynomial is a polynomial of the form $ax+b$, $a≠0$ Thus $3x-1$, $2x-5$, $\frac{3}$

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

3.3B Synthetic Division

A. Linear Polynomials

Linear polynomials are defined as polynomials of the form ax + b, where a ≠ 0.

Example: 3x - 1, 2x - 5, and 3x - 1 are linear polynomials.

B. Monic Polynomials

Monic polynomials are polynomials with a leading coefficient of 1.

Example: x³ + 5x² - 2x - 1, x² - 3x² - 2, and x + b are monic polynomials.

C. Monic Linear Polynomials

Monic linear polynomials are both linear and monic, taking the form x - c.

Example: x + 5, x - 2, and x + 3 are monic linear polynomials.

Highlight: All monic linear polynomials can be written as x - c, where c can be positive, negative, or zero.