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

Algebra ->  Equations -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!

First set up the synthetic division table

i|120-4
|


Start by bringing down the leading coefficient 1

i|120-4
|
1


Multiply i by 1 and place the product (which is i) right underneath the second coefficient (which is 2)
i|120-4
|i
1

Add i and 2 to get i+2. Place the sum right underneath i.
i|120-4
|i
1i+2

Multiply i by i+2 to get i%5E2%2B2i=-1%2B2i and place it right underneath the third coefficient 0
i|120-4
|i-1+2i
1i+2

Add -1+2i and 0 to get -1+2i. Place the sum right underneath -1+2i.
i|120-4
|i-1+2i
1i+2-1+2i

Multiply i by -1+2i to get -i%2B2i%5E2=-2-i and place the product right underneath the fourth coefficient -4
i|120-4
|i-1+2i-2-i
1i+2-1+2i

Add -2-i and -4 to get -6-i. Place the sum right underneath -2-i.
i|120-4
|i-1+2i-2-i
1i+2-1+2i-6-i




Since the remainder is -6-i, this means that f%28i%29=-6-i


In other words, if we plug "i" in for "x" into f%28x%29=x%5E3%2B2x%5E2-4, we'll get -6-i