How many different numbers stisfy the equation (x-2)^2(x-1)^3(x+1)^4(x+2)^5 = 0

Question

I really need help. Thanks!

Answer 1

each factor could be zero, thus

x-2 = 0 ---> x = 2
x-1 = 0 ---> x = 1
x+1 = 0 ---> x = -1
x+2 = 0 ---> x = -2

Look how Wolfram graphed it. How many times and where does the graph intersect with the x-axis ?

Answer 2

oops, forgot the link to the graph

http://www.wolframalpha.com/input/?i=%28x-2%29%5E2%28x-1%29%5E3%28x%2B1%29%5E4%28x%2B2%29%5E5+%3D+0