The completely factored form of 2d^4 + 6d^3 - 18d^2 - 54d is

The first step we take is to factor out a GCF:

2d (d³ + 3d² - 9d - 27)

Now, we can factor what's in the parenthesis by grouping (don't forget to keep the 2d we factored out):

2d[d² (d+3) - 9 (d+3) ]

2d (d²-9) (d+3)

d²-9 can still be factored because it is the difference of two squares:

2d (d+9) (d-9) (d+3)

That is the completely factored form.