1. ## 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!

2. 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 $\displaystyle \frac{x^2 + 4}{x - 2i} = \frac{(x + 2i)(x - 2i)}{x - 2i} = x + 2i$.

3. 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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