Construct a polynomial function with the following properties: fifth degree, 4 is a zero of multiplicity 3, −2 is the only other zero, leading coefficient is 2.

Step-by-step explanation:

Hello, please consider the following.

Construct a polynomial function with the following properties...

... fifth degree

It means that the polynomial can be written as below.

... 4 is a zero of multiplicity 3

We can write the polynomial as below.

... −2 is the only other zero

Because this is the only other zero, we can deduce that -2 is a zero of multiplicity 2.

... leading coefficient is 2.

Finally, it means that k = 2 and then the polynomial function is:

Hope this helps.

Do not hesitate if you need further explanation.

Thank you

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step-by-step explanation: