SOLUTION: Hi, Can you help me with this math problem? Find all of the real and imaginary zeroes for the polynomial function. f(x)=x^3-8x^2+x-8 the answer should be 8,-i,i

Question 135364: Hi,
Can you help me with this math problem?
Find all of the real and imaginary zeroes for the polynomial function.
f(x)=x^3-8x^2+x-8
the answer should be 8,-i,i
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Find all of the real and imaginary zeroes for the polynomial function.
f(x)=x^3-8x^2+x-8
:
x^3 - 8x^2 + x - 8 = 0
:
Factor by grouping
x^3 + x - 8x^2 - 8 = 0
:
x(x^2 + 1) - 8(x^2 + 1) = 0
:
Factor out (x^2+1)
(x - 8) (x^2 + 1) = 0
:
x = +8
and
x^2 = -1
x = +/-Sqrt(-1)
x = +/- i
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