Please help me solve this... Use the given information about a polynomial function to write the equation.
Degree 4. Root of multiplicity 2 at x=-2, and roots with multiplicity of 1 at x=6
and x=2. y-intercept at (0,10)

Step-by-step explanation:

The standard, factored polynomial function is given by:

Where a is the leading coefficient,

p and q are factors,

And n and m are the powers or multiplicity they are being raised to.

We know that our polynomial function is of degree 4.

We have a root of multiplicity of 2 at x=-2.

So, our factor is:

It is has a multiplicity of 2, it is squared. So:

We have another root with multiplicity of 1 at x=6.

So, our factor is:

And since it is to the first power, we can write it as is.

Finally, we have another root of multiplicity of 1 at x=2.

So, our factor is:

Therefore, our entire function is:

We still have to determine our leading coefficient, a.

We can use that y-intercept. The y-intercept is at (0, 10). So, when x=0, y=10. By substitution:

Evaluate:

Multiply:

Therefore:

Therefore, our final function is:

explanation:

step-by-step explanation: