# How do you use synthetic division to divide #(180x-x^4)/(x-6)#?

##### 1 Answer

#### Explanation:

Write

You can only use synthetic division when you are dividing by something in the form of

A picture of my work is attached.

I circled the terms I focus on in each step:

Bring the first number down; here, that's

Step 2: Multiply

Step 3: Multiply that answer by 6:

Add those numbers:

Step 4:Multiply that result by

Step 5: Multiply:

Finally, Multiply

This last number is the remainder. The remainder should always be divisor of the problem (In this case,

On the bottom row, you now have the coefficients of the answer: -1, -6, -36, -36, -216.

We know that

Finally, synthetic division seems a little magical, so I recommend watching Dr. Khan's videos on synthetic division on KhanAcademy. He works through a problem to show why it works. Good luck!