why k is written before some polynomials for example :

k(x^2+4x+4)

Consider the following figure.

 

Here the pink curve depicts the parabola

And the blue curve depicts the parabola

Both the equations of the curve are mulytiples of each other.

 

And the behaviour of these curves are same and they differ only in the constant.

 

This is the reason why we are having constant multiple of polynomials.