Synthetic division

Synthetic division is a way to do math problems that involve dividing. It's kind of like a shortcut that makes it easier to do the problem quickly.

Here's how it works: Let's say you have a big scary math problem like this: 10x^3 + 5x^2 - 2x + 1 divided by x + 2. That looks really complicated, but with synthetic division, we can do it easily.

First, we write down the numbers in a special way. We put the number we're dividing by (in this case, x + 2) outside of a little box, and write the coefficients of the other numbers inside the box, starting with the highest power of x and going down. It looks something like this:

-2 | 10 5 -2 1

The -2 is outside the box, and the other numbers are inside the box. Now, we're going to use synthetic division to do the problem.

First, we take the -2, and we put it under the first number inside the box, which is 10. Then we draw a line underneath the 10 and the -2. It looks like this:

-2 | 10 5 -2 1
-20

We got -20 by multiplying -2 by 10. We write it underneath the line.

Next, we add the 5 and the -20 to get -15. We write that number underneath the -20, like this:

-2 | 10 5 -2 1
-20 -15

Then we multiply -2 by -15 to get 30. We write that number underneath the -15:

-2 | 10 5 -2 1
-20 -15 30

Finally, we add -2 and 30 to get 28. We write that number underneath the 30:

-2 | 10 5 -2 1
-20 -15 30 28

Now we're done with the synthetic division part of the problem. The answer is the numbers we have written down: -20, -15, 30, and 28.

If we put those numbers together, we get this:

10x^3 + 5x^2 - 2x + 1 / (x+2) = 10x^2 - 15x + 30 + 28/(x+2)

So, using synthetic division helped us solve the problem easily and quickly.