What would be the roots of this equation in factored form?

I suppose that "x^3 - 8x^2 + 9 + 18" should be "x^3 - 8x^2 + 9x + 18" instead.

Let f(x) = x^3 - 8x^2 + 9x + 18

f(-1) = -1 - 8 - 9 + 18 = 0
By factor theorem, (x + 1) is a factor of x^3 - 8x^2 + 9x + 18.

x^3 - 8x^2 + 9x + 18
= x^3 + (x^2 - 9x²) + (- 9x + 18x) + 18
= (x^3 + x^2) - (9x² + 9x) + (18x + 18)
= x^2(x + 1) - 9x(x + 1) + 18(x + 1)
= (x + 1)(x^2 - 9x + 18)
= (x + 1)(x - 3)(x - 6)

x^3 - 8x^2 + 9 + 18 = 0
(x + 1)(x - 3)(x - 6) = 0
x + 1 = 0 or x - 3 = 0 or x - 6 = 0
x = -1 or x = 3 or x = 6

y=x^3 - 8x^2 + 9x + 18
=(x+1)(x-3)(x-6)

see step by steps solution for x^3 - 8x^2 + 9x + 18 = 0:
https://www.symbolab.com/solver/step-by-step/x%5E%7B3%7D%20-%208x%5E%7B2%7D%20%2B%209x%20%2B%2018%20%3D%200/?origin=button

hope this helps

I am guessing that the equation has a typo. If 9 is the coefficient of x, then -1 is a root. Use synthetic division to factor (x + 1) from the polynomial. The other factor will be quadratic. Deal with that as you will.

x^3-8x^2+27=0