What are the roots of the polynomial equation x^3-3x^2-6x+8

Ve must factor

factor by grouping
hmm
erm
(trial and error)

if we group it like this:
(-3x^2-6x)+(x^3+8)
we can factor each group
the first is a -3x
the 2nd is a sum of 2 perfect cubes
(-3x)(x+2)+(x+2)(x²-2x+4)
undistribute (x+2) from each
(x+2)(-3x+x²-2x+4)
(x+2)(x²-5x+4)
can we factor more?
what 2 numbers multiply to get 4 and add to get -5?, -1 and -4
(x+2)(x-1)(x-4)

set eqch to zero (assuming it is equal to 0)

0=(x+2)(x-1)(x-4)

0=x+2
-2=x

0=x-1
1=x

0=x-4
x=4

x=-2, 1, 4

In all honesty, there really is no “work” per say to show. mainly it’s just using the process of elimination. the question is asking which domain(s) would be the most appropriate for the function c(n). n is the number of observed vehicles so right away, 1, 2, and 3 can be eliminated.why? 1, 2 start in the negatives and therefore it is impossible to observe negative cars. so, #4 would be the best answer to the given problem.