SOLUTION: Use synthetic division to determine f(i) if f(x)=x^3+2x^2-4 any help would be appreciated, thank you! oh by the way here are the choices to choose from: A.-5-2i B.-5+2i

Question 189557: Use synthetic division to determine f(i) if f(x)=x^3+2x^2-4
any help would be appreciated, thank you!
oh by the way here are the choices to choose from:
A.-5-2i
B.-5+2i
C.-6+i
D.-6-i
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

First set up the synthetic division table

i	\|	1	2	0	-4
	\|

Start by bringing down the leading coefficient 1

i	\|	1	2	0	-4
	\|
		1

Multiply i by 1 and place the product (which is i) right underneath the second coefficient (which is 2)

i	\|	1	2	0	-4
	\|		i
		1

Add i and 2 to get i+2. Place the sum right underneath i.

i	\|	1	2	0	-4
	\|		i
		1	i+2

Multiply i by i+2 to get and place it right underneath the third coefficient 0

i	\|	1	2	0	-4
	\|		i	-1+2i
		1	i+2

Add -1+2i and 0 to get -1+2i. Place the sum right underneath -1+2i.

i	\|	1	2	0	-4
	\|		i	-1+2i
		1	i+2	-1+2i

Multiply i by -1+2i to get and place the product right underneath the fourth coefficient -4

i	\|	1	2	0	-4
	\|		i	-1+2i	-2-i
		1	i+2	-1+2i

Add -2-i and -4 to get -6-i. Place the sum right underneath -2-i.

i	\|	1	2	0	-4
	\|		i	-1+2i	-2-i
		1	i+2	-1+2i	-6-i

Since the remainder is -6-i, this means that

In other words, if we plug "i" in for "x" into , we'll get
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