Master dividing two polynomials using synthetic division
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Master dividing two polynomials using synthetic division

From basic to the most advanced. You will learn how divide two polynomials using synthetic division.
0.0 (0 ratings)
Instead of using a simple lifetime average, Udemy calculates a course's star rating by considering a number of different factors such as the number of ratings, the age of ratings, and the likelihood of fraudulent ratings.
26 students enrolled
Created by Brian McLogan
Last updated 2/2015
English
Price: Free
Includes:
  • 1 hour on-demand video
  • 2 Supplemental Resources
  • Full lifetime access
  • Access on mobile and TV
What Will I Learn?
  • Students will be able to identify the divisor, dividend, quotient, and remainder
  • Students will be able to rewrite a division problem using the remainder theorem
  • Students will be able to divide two polynomials using long division
  • Students will be able to rewrite a polynomial in descending power form
View Curriculum
Requirements
  • Pre-algebra
  • Algebra 1
  • Solving quadratics
  • Operations of polynomials
Description

Math is life – everything we do in our day-to-day lives involves math in some way, whether we realize it or not. Dividing two polynomials is definitely not an exception, and understanding how to do it will open up a world of graphic solutions, algebraic processes, and even life solutions.

But none of that means anything if you don’t have an easy way of understanding it. That’s where this three-part course comes in.

Introduction – To start things out, I’ll use sample videos and worksheets to give you simple definitions, process outlines, and some basic questions to help you build up an understanding of how to solve linear equations. Even if you’ve tried to learn this before, we’ll start from scratch to get you on the right foot.

Examples – Understanding is all about applying and testing, so next you’ll work through some examples to help drive in what you learned in the first section about dividing polynomials using long division. This isn’t about getting a passing grade, so there’s no stress to get everything right. Complete the whole worksheet if you can, or just pick the problems you know you need to work on, and check your answers against a short step-by-step tutorial that shows you how to get from problem to solution.

Conclusion – Finally, you’ll get another worksheet of questions to discuss, reflect on, and answer to really drive in what you’ve learned and ensure you’ve got it in the long run. For those who want to move on to the next course, there are even challenge problems to get you ready. But mostly, this section is about making sure you’re ready for real-world application, not just finishing a worksheet. It’ll all come together in a final summary video where I point out common mistakes plus tips and little-known tricks to help you along in the future when determining the zeros of a polynomial.

This course should only take a couple days, but what you learn will help you for the rest of your life. All at a tiny fraction of what a tutor would cost, and right from the comfort of a home laptop, tablet, or phone. No driving, no anxiety, no pressure, all for under $10 with a 30-day money-back guarantee.

See how much simpler math can be. Sign up today to get started!

Who is the target audience?
  • Algebra 2 students
  • Pre-Calculus students
  • Anyone willing to learn
Students Who Viewed This Course Also Viewed
Curriculum For This Course
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Introduction
2 Lectures 03:19

This lecture will explain all of the basic techniques and understandings you will need to be successful in this course.

What do I need to know?
03:19

Essential questions are provided to give you an idea of what the focus of understanding will be for the course. Print out and answer before and after you take the course.

Essential questions
1 page
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Essential Definitions and Processes
2 Lectures 08:10
What is synthetic division
03:37

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

How to divide two polynomials using synthetic division
04:33
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Examples
17 Lectures 45:24
Problems
1 page

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 1
02:31

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 2
03:06

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 3
03:17

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 4
03:02

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 5
03:23

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 6
01:55

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 7
02:43

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 8
02:00

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 9
02:26

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 10
02:21

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 11
02:24

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 12
04:32

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 13
03:07

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 14
02:16

When dividing two polynomials using synthetic division it is very important to verify that your divisor is a linear factor. Otherwise you will have to use long division to obtain the quotient. The next step is to arrange your dividend in descending power order and to determine your zero by setting up your factor to zero and solving for your variable. You will now arrange the coefficients of your polynomial inside of a box and your zero integer outside of the box in the upper left hand corner. For the first coefficient you will drop down below the box and then multiply by your integer. Take that product and place it below your next coefficient and determine the sum. Take the sum and multiply agin my your zero integer and repeat the process until you cannot add the sum to any more coefficients. If your last sum is zero then your divisor evenly divides into your dividend and the quotient is another factor of the polynomial. If there is a number other than one then that number is called our remainder. To determine the factor from the quotient simply start from the right side and label the first number the constant. Second number the coefficient of the linear term, next number the coefficient of the quadratic term and keep going till there are no more coefficients.

Divide two polynomials using synthetic division ex 15
04:03

Divide two polynomials using synthetic division ex 16
02:18
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Conclusion
0 Lectures 00:00
About the Instructor
Brian McLogan
4.2 Average rating
26 Reviews
860 Students
8 Courses
Current Active High School Math Teacher

I am a high school that is on a mission to improve math education. I was that student that sat in the back of class frustrated with the boredom of class and the lack of understanding. I made the decision to become a math teacher to make a difference in others lives. I knew that with the struggles I had I could relate well to students that struggled with math. With a weak math background I set out to get a degree in mathematics. In was a difficult journey and I worked very hard not just to pass my math classes but to have an understanding of what I was doing. I learned a lot about myself, mathematics and what it takes to be successful in class through my time at college. I want to pass along my experience to you the student so that may have your own success with mathematics.