Question

(6m^3 -16m^2 + 15m - 40) / (2m^2 + 5)

Answer 1

        6m3 - 16m2 + 15m - 40 Simplify ————————————————————— 2m2 + 5 Checking for a perfect cube :

 4.1    6m3 - 16m2 + 15m - 40  is not a perfect cube 

Trying to factor by pulling out :

 4.2      Factoring:  6m3 - 16m2 + 15m - 40 

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  15m - 40 
Group 2:  -16m2 + 6m3 

Pull out from each group separately :

Group 1:   (3m - 8) • (5)
Group 2:   (3m - 8) • (2m2)
               -------------------
Add up the two groups :
               (3m - 8)  •  (2m2 + 5) 
Which is the desired factorization

3m-8 is the answer