SOLUTION: Given P(x)= x^4-2x^3+7x^2-18x-18 These are the question i need help with A)show that -3i is a root of P(x) B)Factor P(x) into linear factors

Algebra ->  Rational-functions -> SOLUTION: Given P(x)= x^4-2x^3+7x^2-18x-18 These are the question i need help with A)show that -3i is a root of P(x) B)Factor P(x) into linear factors      Log On


   

Question 270279: Given P(x)= x^4-2x^3+7x^2-18x-18
These are the question i need help with
A)show that -3i is a root of P(x)
B)Factor P(x) into linear factors
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hints:

A) Simply plug in x=-3i and show that doing so will result in 0. In other words, show that P%28-3i%29=0

B) Since -3i is a root, 3i is also a root. This means that x%5E2%2B9 is a factor. Now use x%5E2%2B9 to factor x%5E4-2x%5E3%2B7x%5E2-18x-18+ (use polynomial long division) into two quadratics. Factor the resulting quadratic further if possible.