Welcome to the forum.

In the screen shot below I have shown my layout for this. (note: it will be beneficial to keep terms in neat columns)

(i) I re-ordered the terms to start with the highest power of x, and then in descending powers. Make sure the signs go with the terms.

(ii) Ask what must I multiply by x to get

(iii) now multiply (x + y - z) by this amount and put the results below. Line up matching terms to make the subtraction easier.

(iv) Subtract and write in the remaining terms.

(v) Ask what must I multiply by x to get

(vi) Subtract to get the remainder. This is zero so the division is complete.

Hope that helps,

Bob

]]>Are you supposed to do it by hand?

]]>Divide (4x^3yz^3+3x^4y^2z+4x^2y^2z^3+3x^3y^3z-4x^2yz^4-3x^3y^2z^2) by (x+y-z)]]>