Question

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a. -2 with multiplicity 1,0 with multiplicity 2, and 3 with multiplicity 3
b. -2 with multiplicity 1,0 with multiplicity 2, and 3 with multiplicity 1
c. 2 with multiplicity 1,0 with multiplicity 3, and -3 with multiplicity 1
d. -2 with multiplicity 1,0 with multiplicity 3, and 3

Explanation:

Step1: Identify x-intercepts

The graph crosses/touches x-axis at $x=-2$, $x=0$, $x=3$.

Step2: Analyze multiplicity at $x=-2$

Graph crosses axis, so multiplicity = 1.

Step3: Analyze multiplicity at $x=0$

Graph touches axis (flattens, turns around), so multiplicity = 2.

Step4: Analyze multiplicity at $x=3$

Graph crosses axis, so multiplicity = 1.

Answer:

B. $-2$ with multiplicity 1, $0$ with multiplicity 2, and 3 with multiplicity 1