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Answer:
The exponent is 2.
Step-by-step explanation:
Remember multiplicity rules:
- If a factor has an odd multiplicity (e.g. it is raised to 1, 3, 5...) then it will cross the x-axis.
- If a factor has an even multiplicity (e.g. it is raised to 2, 4, 6...) then it will bounce off the x-axis.
At x=2, we have the factor (x-2).
From the graph, we can see that the graph bounces off at that point.
Hence, the multiplicity of (x-2) must be even.
Therefore, a possible exponent for the factor (x-2) is 2. Any even number will suffice.