How do you find all solutions real and complex on the following problem?
f(x)= (x^5)-(5x^4)+(12x^3)-(24x^2)+(32x)-16
The first value I tried was f(1) and I got a zero.
So x-1 is a factor,
I then tried f(2) and again got a zero,
so x-2 was a factor.
by Synthetic division by first x-1 and then x-2 I was left with
x^3 - 2x^2 + 4x - 8 which "groups" nicely to
x^2(x-2) + 4(x-2)
=(x-2)x^2+4)
so f(x) = (x-1)x-2)(x-2)(x^2+4)
Can you take it from here?