Verified answer

Factor out the common factor:

2x (x^3 - 31x + 30)

Look at the graph of y = x^3 - 31x + 30 or use the rational roots theorem to find the zeros at x = -6, x = 1 and x = 5.

Use the factor theorem to convert these zeros into factors:

(x + 6) (x - 5) (x - 1)

So altogether the factorization is:

2x (x + 6) (x - 5) (x - 1)

2x^4 - 62x² + 60x

x(2x^3 - 62x + 60)

2x(x-5)(x+6)(x-1)