Question 63773
polynomial must be  6m^2 -19mn +10n^2

here we use middle term breaking 

first multiply coefficient of m^2 & n^2
 here it is +60
 if it is positive then just break 60 in two factors so that sum of two is 19
 here 60 = 15*4
   
  6m^2 -19 mn + 10n^2

= 6m^2 -(15+4)mn +10 n^2

= 6m^2 -15mn -4mn + 10n^2

= 3m(2m - 5n) -2n(2m - 5n)

=(2m-5n)(3m-2n)