Explanation:
all coefficients are integers, the rational zeros theorem can be applied.
that means each rational solution ("root") x = p/q, written in most simplified terms so that p and q are relatively prime, can be found for the polynomial
an×x^n + an-1×x^(n-1) + ... + a1×x + a0
p is an ± integer factor of the constant term a0, and
q is an ± integer factor of the leading coefficient an.
in our case here
an = a4 = 1
a0 = 8
the only factor for 1 is ±1.
the factors for 8 are
±1, ±2, ±4, ±8
so, we get
1/1, 2/1, 4/1, 8/1, -1/1, -2/1, -4/1, -8/1, 1/-1, 2/-1, 4/-1, 8/-1, -1/-1, -2/-1, -4/-1, -8/-1
that leaves us with the different values of
1/1, 2/1, 4/1, 8/1, -1/1, -2/1, -4/1, -8/1
sorted from smallest to largest
-8/1, -4/1, -2/1, -1/1, 1/1, 2/1, 4/1, 8/1
or simply
-8, -4, -2, -1, 1, 2, 4, 8