For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the
x-axis at each x -intercept.
-
A)-4, multiplicity 1, crosses x-axis; 4, multiplicity 2, touches x-axis
B)4, multiplicity 1, crosses x-axis; -4, multiplicity 2, touches x-axis
C)-4, multiplicity 1, touches x-axis; 4, multiplicity 2, crosses x-axis
D)4, multiplicity 1, touches x-axis; -4, multiplicity 2, crosses x-axis

Question

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the
x-axis at each x -intercept.
-
A)-4, multiplicity 1, crosses x-axis; 4, multiplicity 2, touches x-axis 
B)4, multiplicity 1, crosses x-axis; -4, multiplicity 2, touches x-axis 
C)-4, multiplicity 1, touches x-axis; 4, multiplicity 2, crosses x-axis 
D)4, multiplicity 1, touches x-axis; -4, multiplicity 2, crosses x-axis

Quizplus · Accepted Answer

The polynomial has three real roots: -4 with multiplicity 1, and 4 with multiplicity 2. Because the multiplicity of -4 is 1, the graph crosses the x-axis at that root. However, because the multiplicity of 4 is 2, the graph only touches the x-axis at that root (it bounces off and continues). Choice A correctly identifies these roots and their multiplicities, as well as the nature of the graph at each root.

For the Polynomial, List Each Real Zero and Its Multiplicity