I'm sure every e2 user has, at one point in their life, asked themselves the question, "Is there any way to make polynomial long division even better than it already is?" Wonder no longer, for here I present to you the secret to synthetic division.

Synthetic division is basically long division condensed. It can be used on polynomial equations of any degree as long as the divisor is of the form x + c where c is a constant. For example, if you are given the polynomial expression:

3x4 + 2x3 - 5x2 - 6x + 4

and you want to divide by x-2. Set up for synthetic division as follows:

```                   2    |    3      2      -5     -6     4
|
|
___________________________________

```

The first number, before the pipe, is -c from the divisor. The numbers that follow are the coeffients from the polynomial expression. Note: Every "degree" must be represented, for example if the expression was 3x4 + 2x3 - 6x + 4

, instead of the -5, there should be a zero. Skipping over it entirely is not a good thing.

Now we shall proceed. First bring the first number down below the line like so.

```                   2    |    3      2      -5     -6     4
|
|
___________________________________
3
```

Now multiply that number by the number in the box, in this case 2. Place that number beneath the next term, add them, and place the result underneath the line.

```                   2    |    3      2      -5     -6     4
|
|           6
___________________________________
3      8
```

Continue this process, this time multiplying 8 by 2, placing it beneath -5, adding and placing the result beneath the line.

```                   2    |    3      2      -5     -6     4
|
|           6      16
___________________________________
3      8      11
```

The final result should look like this:

```                   2    |    3      2      -5     -6     4
|
|           6      16     22     32
___________________________________
3      8      11     16     36
```

How to interpret this strange mess? Easy! The resulting polynomial expressing is characterized by the numbers below the line, which represent the coefficients. In this case, you're left with 3x3 + 8x2 + 11x + 16, and a remainder of 36.