Dividing a polynomial by a monomial: Multivariate

Divide.
\[
\frac{-14 u^{6} z+12 u^{6} z^{4}}{-3 u^{3} z^{2}}
\]

Simplify your answer as much as possible.

Step 1 ：Define the variables u and z.

Step 2 ：Define the polynomial as -14 * u^6 * z + 12 * u^6 * z^4 and the monomial as -3 * u^3 * z^2.

Step 3 ：Divide the polynomial by the monomial to get the result.

Step 4 ：The result from the division is a tuple with two elements. The first element is the quotient of the division and the second element is the remainder.

Step 5 ：In this case, the remainder is -14*u^6*z, which means that the division is not exact. However, the problem asks to simplify the answer as much as possible, so we should only consider the quotient, which is -4*u^3*z^2.

Step 6 ：The simplified result of the division is \(\boxed{-4 u^{3} z^{2}}\).