What is synthetic division

Instead of writing a positive 4, we write the negative of that. So we write the negative, which would be negative 4. And now we are all set up, and we are ready to perform our synthetic division. And it's going to seem like voodoo. In future videos, we'll explain why this works. So first, this first coefficient, we literally just bring it straight down. And so you put the 3 there. Then you multiply what you have here times the negative 4.

So you multiply it times the negative 4. Then you add the 4 to the negative Then you multiply negative 8 times the negative 4.

I think you see the pattern. Negative 8 times negative 4 is positive Now we add negative 2 plus positive That gives us positive Then you multiply the positive 30 times the negative 4. And that gives you negative And then you add the negative 1 plus the negative And you end up with a negative Now the last thing you do is say, well, I have one term here. And in this plain, vanilla, simple version of synthetic division, we're only dealing, actually, when you have x plus or minus something.

Add the terms of the second column. Multiply the result by k. Repeat steps 5 and 6 for the remaining columns. Use the bottom numbers to write the quotient. The number in the last column is the remainder and has degree 0, the next number from the right has degree 1, the next number from the right has degree 2, and so on. Show Solution Begin by setting up the synthetic division. Write k and the coefficients. Show Solution Notice there is no x term.

Show Solution There are a few ways to approach this problem. Did you have an idea for improving this content? Licenses and Attributions. CC licensed content, Original. Example 4 : Use synthetic division to divide by x - 2. Use the result to find all zeros of f. This time, we are looking for all of the zeros of f. We will start by dividing using synthetic division and then rewrite f x as x - 2 quotient. Using synthetic division to find the quotient we get: Note how the remainder is 0.

This means that x - 2 is a factor of. Practice Problems. At the link you will find the answer as well as any steps that went into finding that answer. Practice Problem 1a: Divide using synthetic division. Practice Problem 2a: Given the function f x , use the Remainder Theorem to find f Need Extra Help on these Topics? The following are webpages that can assist you in the topics that were covered on this page:. All rights reserved. After completing this tutorial, you should be able to: To divide a polynomial by a binomial of the form x - c using synthetic division.

In this tutorial we are going to look at synthetic division. Synthetic division is another way to divide a polynomial by the binomial x - c , where c is a constant. Step 4: Add the column created in step 3.

Step 5: Repeat until done. Long division would look like this:. Example 2 : Divide using synthetic division:. Definition of synthetic division. First Known Use of synthetic division , in the meaning defined above. Learn More About synthetic division. Share synthetic division Post the Definition of synthetic division to Facebook Share the Definition of synthetic division on Twitter.

Time Traveler for synthetic division The first known use of synthetic division was in See more words from the same year. Dictionary Entries Near synthetic division synthetic detergent synthetic division synthetic fiber See More Nearby Entries. Statistics for synthetic division Look-up Popularity.