The polynomial of degree 3, p(x), has a root of multiplicity 2 at x=5 and a root of multiplicity 1 at x=−5.
the y-intercept is y=−87.5.
find a formula for p(x).
p(x)=

P(x) =

Step-by-step explanation:

Root multiplicity of 2 means the root is repeated 2 times. Root multiplicity of 1 means root is repeated only once.

A polynomial of degree 3 means the largest exponent of x is 3.

Here, the polynomial P(x) has root 5 with multiplicity 2 and -5 with multiplicity 1.

So, P(x) =

Where, is a constant.

Now, it's given that the y intercept is -87.5. Therefore, value of x at y intercept is 0.

We obtain by plugging in -87.5 for P(x) and 0 for x.

Therefore, the polynomial P(x) is given as:

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step-by-step explanation:

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the first option is the answer.