factor by grouping if possible and check

5x^3+4x^2-10x-8

5x^3+4x^2-10x-8

Note that the coefficients are
5,4, -10,-8
with 5,4 as a common factor
=5,4, -2(5,4)
So we can factorize by grouping.

5x^3+4x^2-10x-8
=x^2(5x+4) -2(5x+4)
Taking (5x+4) as the common factor
=(x^2-2)(5x+4)
would be the answer for rational factors.
Further factoring into
(x+√2)(x-√2)(5x+4)
is possible but two of the factors are not rational.

which are in the same proportion