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