# Synthetic Division

• Aug 3rd 2009, 05:26 PM
tecktonikk
Synthetic Division
How do you do synthetic division to find

(x^2 + 4) Divided By (x-2i)

and

f(x)= x^3 -3x^2 +x -3

zero at x = 3

I learn by examples, so please show work!
If you don't want to tell me the answer, just give a example similar to the problems above and the answer and steps to solve the example problem.
Thank You Very Very much!
• Aug 3rd 2009, 05:32 PM
Prove It
Quote:

Originally Posted by tecktonikk
How do you do synthetic division to find

(x^2 + 4) Divided By (x-2i)

and

f(x)= x^3 -3x^2 +x -3

zero at x = 3

I learn by examples, so please show work!
If you don't want to tell me the answer, just give a example similar to the problems above and the answer and steps to solve the example problem.
Thank You Very Very much!

Note that

$\displaystyle x^2 + 4 = x^2 - (2i)^2 = (x + 2i)(x - 2i)$

So $\displaystyle \frac{x^2 + 4}{x - 2i} = \frac{(x + 2i)(x - 2i)}{x - 2i} = x + 2i$.
• Aug 3rd 2009, 09:08 PM
yeongil
You can still use synthetic division to divide $\displaystyle (x^2 + 4) \div (x-2i)$:
Code:

2i|  1  0  4 --      2i  -4   ------------     1  2i  0
So the quotient, as Prove It has shown, is $\displaystyle x + 2i$.

For the second problem, I'm guessing that you're being asked to show that
$\displaystyle (x^3 -3x^2 +x -3) \div (x - 3)$ has no remainder. The setup would be like this:
Code:

3| 1  -3  1  -3 --   --------------   1
I'll let you do the rest. If you're stuck, look at this tutorial on synthetic division here: Synthetic Division .

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