I asked this question previously, but I was told you were unable to get the answer with rational numbers. I asked my teacher, and he said we could use estimates.

Question

y=x^4-4x^3+16
y=(x-2)(x^3-2x^2-4x-8)
so i used 3.68

and i got this (x-2)(x-3.68)(x^2+1.68x+2.1824)

Could someone help me finish?

Answer 1

The remaining quadratic has no solution in the set of real numbers.
The value of b^2 - 4ac in the formula is negative, so we cannot take the √ of a negative number.

your only real solutions are x = 2 and x = appr. 3.68

Answer 2

When you first asked this question, you asked for the factors, you did not ask for a solution to the corresponding equation x^4-4x^3+16 = 0

That is how it was answered.