PreCalculus/Trig Check please and help
posted by Tabitha on .
Could someone please check the first one and help me with the second one. I'm stuckThank you
1.What are theroots of the following polynomial equation?
(x+2i)(x5)(x2i)(x+8) = 0
I think the roots are 2i,5,2i,8you take out the roots as opposites of what are in the equaion correct?
2. Write a polynomial of the smallest degree with roots 3,3i and 3i
Final answer can't have parentheses
(x3)(x3i)(x+3i)=0 and then I'm stuck I don't know what to do when you multiply the x times the 3i

First find (x3i)(x+3i)=x^2+9 and then
(x3)(x^2+9)=x^33x^2+9x27 
Do the last two first: (x3i)(x+3i) You can do FOIL (the anwer to x*(3i) is 3xi), however, notice x+9 is the answer. (x^2+9) is the difference of two squares, x and 3i, so (x^2+9)=(x+3i)*(x3i)
so you now have (x3)(x^2+9)
= x^3+9x 3x^327 Using the FOIL method. 
Whenn I get to (x3)(x^2+9) and FOIL wouldn't it be x^3 +9x3x^2 27? I get (3x^2) not (3x^3) when I multiply 3 times x^2 or am I missing something
Thank you 
correc, typo. 3x^2