Solution - Factoring multivariable polynomials

Step  1  :

Equation at the end of step  1  :

  (((6•(x5))•(y3))+((15•(x3))•(y2)))-(32x4•y3)
 Step  2  :

Equation at the end of step  2  :

  (((6•(x5))•(y3))+((3•5x3)•y2))-32x4y3
 Step  3  :

Equation at the end of step  3  :

  (((2•3x5) • y3) +  (3•5x3y2)) -  32x4y3

Step  4  :

Step  5  :

Pulling out like terms :

 5.1     Pull out like factors :

   6x⁵y³ - 9x⁴y³ + 15x³y²  =   3x³y² • (2x²y - 3xy + 5) 

Trying to factor a multi variable polynomial :

 5.2    Factoring    2x²y - 3xy + 5 

Try to factor this multi-variable trinomial using trial and error 

 Factorization fails

Final result :

  3x3y2 • (2x2y - 3xy + 5)