Answer:
Step-by-step explanation:
The standard form for a polynomial equation in its factored form is:
Where p and q are the zeros and a is the leading coefficient.
We know that the degree of the polynomial is 5.
We are also given roots at x=3 and x=-2. Hence, our factors are (x-3) and (x+2).
These have a multiplicity of two, so we will square them.
We also know that there is a root at x=4. Hence, the factor is (x-4). This has a multiplicity of 1.
Therefore, our polynomial is now:
We know that the y-intercept is 12. Therefore, if we substitute in 0 for x, we should get 12 for y. Here, we are solving for our a. Therefore:
Evaluate:
Evaluate:
Divide both sides by -144:
Hence, our entire polynomial is: