<s>[INST] To find factor of a polynomial equation 
One of the factors of $4x^2+y^2+14x-7y-4xy+12$ is equal to

*

*$2x-y+4$


*$2x-y-3$


*$2x+y-4$


*$2x-y+3$

Step $1$:
$4x^2+y^2-4xy$ can be simplified as $(2x-y)^2$
Step $2$:
$14x-7y$ can be simplified as $7(2x-y)$
and finally
$(2x-y) (2x-y+7) + 12$
I can able to factor to this extent only. however can't able to arrive at the answer.
The answer is given in the book. it states that $4x^2+y^2+14x-7y-4xy+12$ is product of $(2x-y+3)$ and $(2x-y+4)$ I am in need of steps
 [/INST] You can do $2x-y=k$ and then
$$k^2+7k+12=(k+3)(k+4)$$
and then you get
$$(2x-y+3)(2x-y+4)$$
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