SOLUTION: Hi, Factor the polynomial completely and find all its zeros (real and complex). P(x) = x^4-1 I have already tried working the problem but am unsure if I am doing it corre

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Hi, Factor the polynomial completely and find all its zeros (real and complex). P(x) = x^4-1 I have already tried working the problem but am unsure if I am doing it corre      Log On


   

Question 887447: Hi,
Factor the polynomial completely and find all its zeros (real and complex).
P(x) = x^4-1
I have already tried working the problem but am unsure if I am doing it correctly. So far I have gotten this:
P(x) = (x^2+1)(x^2-1)
P(x) = (x^2+1)(x-1)(x+1)
I know this problem is not as complicated as I'm making it and I would appreciate all the help :)
--thanks in advance
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
Your approach is just fine.
P(x) = (x^2+1)(x-1)(x+1)
now, you simply set each term (in parentheses) to zero to find each zero:
x^2+1 = 0
x^2 = -1
x = sqrt(-1)
x = {-i, i}
.
x-1 = 0
x = 0
.
x+1 = 0
x = -1
.
solution:
x = {-i, i, -1 , 0}