5n^3-40n^2+4n-32

Assuming that you want to factor:  5n³ -40n² + 4n - 32

Split this into two groups, the first two and the last two:

                                                  [ 5n³ - 40n² ] + [ 4n - 32 ]

Factor 5n² out of the first two and factor 4 out of the last two:

                                                   [ 5n²(n - 8) ] + [ 4(n - 8) ]

                                                       5n²(n - 8)  +  4(n - 8)

Factor (n - 8) out of the two parts:

                                                           (n - 8)(5n² +  4)

Since 5n² +  4 cannot be factored any furher, we are done.