Question

What is the fundamental theorem of algebra of this polynomial in completed factored form? and how do I graph it?
f(x)=x^5-x^4+x^3-x^2+x-1

Answer 1

it says there should be 5 roots.
f(1) = 1-1+1-1+1-1 = 0
so (x-1) is a factor
by synthetic division I had
(x-1)(x^4 + x^2 + 1)

x^2 = (-1 ± √-3)/2 = (-1 ± i√3)/2

now take √ of that again.
So we get one real root of x=1 and 4 imaginary roots.