Factor the polynomial completely

Question

3x³y-13x²y²⁺4xy³

Answer 1

3x³y - 13x²y² + 4xy³

 

The factors each term have in common are x and y.

 

xy(3x² - 13xy + 4y²) =

 

xy(3x - y)(x - 4y)

Answer 2

First factor out xy from the expression.    This leads to

 

  xy [ 3 x² -13 xy  +4 y² ]     The expression inside the parenthesis is trinomial.  The discriminant is  

          169 y² - 121 y²  =  121 y²     which is a perfect square, so the trinomial can be factored.

      With some trial and error, the factoring can be seen to be

 

    xy (3 x - y ) ( x-4 y)