SOLUTION: This is a problem off of the practice equation problems from this site. I started to work out this problem: 2x^4-54x. I got as far as 2x(x^3-27). I couldn't figure out how they mov

Question 66007: This is a problem off of the practice equation problems from this site. I started to work out this problem: 2x^4-54x. I got as far as 2x(x^3-27). I couldn't figure out how they moved from that to the answer of 2x(x-3)(x^2+3x+9)
Can you show the steps on how to get that final answer? I tried to figure it out on my own, but I wasn't even close. Thanks!
Found 2 solutions by Cintchr, Earlsdon:
Answer by Cintchr(475) (Show Source):
You can put this solution on YOUR website!

factor out a 2x

look at the portion in the paranthesis.

This is the difference of two cubes.
There are 2 different "special patterns" to memorize here.
One for the sum of two cubes, the other for the difference of two cubes.
1.
2.
We are using the second formula/pattern

the cube root of x^3 = x
the cube root of 27 = 3

Answer by Earlsdon(6103) (Show Source):
You can put this solution on YOUR website!
Factor:
Factor the 2x as you did.
Now you may recognise the parentheses as the difference of two cubes for which the factored form is:
Apply this to your equation: A = x and B = 3
=