Factorization of multivariable polynomial

I have a multivariable polynomial, for instance: $P=yx+2^4xy+3+5^2xz+3^4zx $

I would like to do the following:

1. extract those terms that only have $z$

2. extract terms that only have $y$

3. express my polynomial something like this: $P=z(…)+y(…)+(some constants)$

I know it’s quite easy but this is just an example what I want to do. In reality, I have a polynomial with 60 terms, so I would like to know the procedure for doing this.