At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x axis?

a. -5
b. -2
c. 2
d. 5

The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.
(x - 5)^3 has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.
(x + 2)^2 has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.
To find where it will touch the axis set the factor equal to zero and solve.
(x + 2) = 0
subtract 2 from both sides
x = -2