1. Consider the polynomial function.
f(x)= x^4 − 2x^3 + 11x^2 + 5x +6
Which statement correctly describes the number of possible positive zeros and the number of possible negative zeros?
a. The number of positive zeros is either 3 or 1. The number of negative zeros is either 2 or 0.
b. The number of positive zeros is either 2 or 0. The number of negative zeros is either 2 or 0.
c. The number of positive zeros is 1. The number of negative zeros is either 3 or 1.
d. The number of positive zeros is either 3 or 1. The number of negative zeros is 1.
2. Consider the polynomial function.
f(x)= x^3(x−2)^2(x+5)
Which statements correctly describes the behavior of the graph of the function at its zeros?
a. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −5 and crosses straight through the x-axis at 2.
b. The graph of the function crosses through the x-axis at 2 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 0 and crosses straight through the x-axis at −5 .
c. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at 2 and crosses straight through the x-axis at −5
d. The graph of the function crosses through the x-axis at 0 and behaves in a cubic fashion. The graph of the function touches and bounces off of the x-axis at −2 and crosses straight through the x-axis at 5.
