SOLUTION: Use the rational zero theorem to find all possible rational zeros, complete the factorization, and solve the corresponding polynomial equation. Be sure to show the synthetic divis

Question 851305: Use the rational zero theorem to find all possible rational zeros, complete the factorization, and solve the corresponding polynomial equation. Be sure to show the synthetic division and find all real and imaginary zeros.
f(x)= x^4-6x^3+14x^2-14x+5
I know that 1 is a rational zero and that 5 is not a rational zero. My teacher commented that since 1 was a rational zero that it may have the multiplicity of 2. From there I have no clue, my answer seems way too long to be correct.
Thank you in advance for helping me.
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
Your teacher meant that 1 might be a zero twice.
(x-1)^2 could be a factor
f(x) = (x-1)^2 (x^2-4x+5)
(x-1)^2=0 x=1and x=1
(x^2-4x+5)=0
x = 2+i
x = 2-i
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