Pls help me out ! i’ll mark you brainliest

This is my question~~ ( r ^ 4 - 2r ^ 3 - 23 r ^ 2 - 4r - 32)÷(r+4) ~~ i must use long division to solve it : / i was wondering if anyone world like to solve it. and if so, share step-by-step explanations! you! ❤

1- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis.2- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in the first question?

Rationalize the denominator- 12x/√x-10