Question

If the graph of the function f has a multiple zero at x = 2, what is a possible exponent of the factor x - 2? Justify your reasoning.
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Answer 1

Answer:

$(x-2)^2$

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.