How do you factor by grouping 11x^2 + 33x - xy - 6y?

Jun 5, 2015

I do not believe there are any rational factors for $11 {x}^{2} + 33 x - x y - 6 y$ (Somebody correct me on this).

Perhaps the $- 6 y$ was meant to be $- 3 y$ (?)

Jun 5, 2015

It looks to me like a factor of $2$ has been accidentally omitted from the $- x y$ term in the expression. That seems to me to be more likely than the alternatives.

If I am correct, the question should be:

How do you factor by grouping $11 {x}^{2} + 33 x - 2 x y - 6 y$?

$11 {x}^{2} + 33 x - 2 x y - 6 y$

$= \left(11 {x}^{2} + 33 x\right) - \left(2 x y + 6 y\right)$

$= 11 x \left(x + 3\right) - 2 y \left(x + 3\right)$

$= \left(11 x - 2 y\right) \left(x + 3\right)$