You are expected to know a few things . . .
This is a seventh-degree polynomial . . . It will have seven zeros.Given: .
1. How many zeros does the polynomial have?
. . [They may not be distinct or real.]
There are three distinct zeros: .2.What are the distinct zeros?
3.Give the multiplicity of each zero.
The multiplicity of each factor is given by its exponent.
has multiplicity 2
has multiplicity 3.
has multiplicity 2.
4. Which zeros cross the x-axis?
5. Which zeros touch the x-axis?
If the multiplcity is odd, the graph cross the x-axis.
If the multiplicity is even, the graph is tangent to the x-axis.
. . Got it?