Factoring help, please help!! just need an explanation?

Question

Factoring help, please help!! just need an explanation?
I was wondering how to factor 3xy^2-11xy+6x, my problem isnt with the numbers but rather its wit the leters. Please show the steps and explain thanks

my bad stupid mistake by me from rushing lol, fgot to factor the x out

Answer 1

3xy^2-11xy+6x
=x(3y^2-11y+6)
=x(3y^2-9y-2y+6)
=x{3y(y-3)-2(y-3)}
=x(y-3)(3y-2)

Answer 2

3xy^2 - 11xy + 6x =
x(3y^2 - 11y + 6) =
(x/3)(y^2 - (11/3)y + 6) =
(x/3)(y^2 - (11/3)y + (11/6)^2+ - (11/6)^2 + 2) =
(x/3)(y^2 - 11/6)^2+ - 121/36 + 72/36) =
(x/3)(y^2 - 11/6)^2+ - 49/36) =
(x/3)(y^2 - 11/6 - 7/6)(y^2 - 11/6 + 7/6) =
(x/3)(y^2 - 18/6)(y^2 - 4/6) =
(x/3)(y^2 - 3)(y^2 - 2/3) =
x(y^2 - 3)(3y^2 - 2)

Answer 3

the only thing that is common to all 3 parts is x

as 11 and 2 are both prime and y does not appear in 6x

therefore it can be written as

x(3y^2-11y+6)

Hope that helps

Answer 4

= (3xy^2 - 11xy + 6x) / x
= (3y^2 - 11y + 6 ) / (y - 3)
= 3y - 2

= x(y - 3)(3y - 2)