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yes but how did you get those numbers

ok

I repeated x = -2 twice by accident in the explanation above.
Anyway, to show x = -2 results in a 0:
(-2)^4+8(-2)^3+7(-2)^2-40(-2)-60 =
16 - 64 + 28 + 80 - 60 = 0
So if x = -2, that means (x + 2) must be a factor of the original polynomial. Division yields (see attached file).
Our new polynomial is x^3 + 6x^2 - 5x - 30. We can use the same Rational Roots Theorem to determine the remaining possible rational root(s).