Expert: Richard J. Raridon - 3/4/2011

Question
Hello,
I am taking an on-line college algebra course and and stumped on these two exercises. I am grasping the process but am not multiplying/substituting correctly because I keep coming up with the wrong answers (it's multiple choice). I've emailed my instructor for help to but she's slow to reply...
Thank you in advance for any help you can provide!

1) Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.

Zeros of 3, i, -i and P(2) = 30

2) Find a polynomial of lowest degree with only real coefficients and having the given zeros.

1 - square root of 3, 1 + square root of 3, and 1 + i

Answer
1) factors are (x-3) and (x^2+1) so if you multiply those together you get
P(x) = x^3-3x^2+x-3 so that P(2) = -5.  Therefore, you have to multiply each term by -6 to get
P(x) -6x^3+18x^2-6x+18
2) if one zero is 1+i you have to have another zero 1-i so the factors are
(x^2-2x-2) and (x^2-2x+2) and the polynomial is x^4-4x^3+2x^2-2x-4