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.