Horner scheme

Horner scheme is a way to do math without needing to write down a bunch of big numbers. Let's say that you have a really big math problem that looks like this: 7x³ + 5x² + 2x - 1. Instead of doing a lot of multiplication and addition with these big numbers, you can use the Horner scheme to make your life easier.

First, you need to pick a number to put into the equation. Let's say that we want to use the number 2. Then, write down the number 2 to the left of the equation:

2 | 7 5 2 -1

Now, we're going to do some simple math. First, we take the number on the left (which is 2) and multiply it by the number on the right (which is 7). The result is 14. Then, we take the next number horizontally and add to the result. This means, we take 14 and add 5 to it. The result is 19. We repeat this step until we reach the end of the numbers.

So, we take 19 and multiply it by 2, then add 2 to it. The result is 40. Finally, we add -1 to the result, giving us a final answer of 39.

So, instead of doing a lot of multiplication and addition with big numbers, we used the Horner scheme to make it easier by multiplying and adding simple numbers.