Answer:

(-1,0),(0,0)(2,0), and (3,0)

Step-by-step explanation:

f(x) = x(x + 1)(x - 3)²(x - 2)

when it touches the x axis is when y is 0

so

0 = x(x + 1)(x - 3)²(x - 2)

and there are four possible x values that make y = 0

x = -1,0,2,3

so the points where f(x) = x(x + 1)(x -  3)²(x - 2) will touch the x axis are points.

(-1,0),(0,0)(2,0), and (3,0)