Consider p(x) = x4(x − 2)3(x + 1)2. for each zero, determine if the graph crosses the x-axis. how do you know?

To find zeros of this polynomial, set the poly = to zero and solve the resulting equation for x.  

Please clarify this:  does your "x4" mean x^4 (x to the 4th power), or something else?

Very important:  for clarity use the symbol " ^ " to indicate exponentiation.

My educated guess is that by "P(x) = x4(x − 2)3(x + 1)2" you actually meant 

P(x) = x^4(x − 2)^3(x + 1)^2, which is a 6th order polynomial.

Set this equal to zero and attempt to solve the resulting equation for x.  You should expect to find up to six zeros (or solutions).