Given the following polynomial, find a. the zeros and the multiplicity of each b. where the graph crosses or touches the x-axis c. number of turning points d. end behavior f(x)= (x−2)^3

Question

Given the following polynomial, find a. the zeros and the multiplicity of each b. where the graph crosses or touches the x-axis c. number of turning points d. end behavior  f(x)= (x−2)^3

anonymous · Answer

We can find the roots of a polynomial by looking at the factors. In this case, the factors  are (x-2)(x-2)(x-2). So, there is only one distinct root since all the factors are the same. We get the root by setting a factor equal to zero. x-2=0 or x=2. So 2 is a root.

Since the factor is repeated three times, it has a multiplicity of three.