Question

Determine the equation of the polynomial, f(x), of minimum degree whose graph is shown above. Write your answer in factored form.

f(x)=____

Answer 1

`f(x)=(5)/(6)(x+2)^2(x-1)(x-3)`

Explanation:

The root -2 has a multiplicity of 2, and corresponds to a factor of
`(x+2)^2`.

The root 1 has a multiplicity of 1, and corresponds to a factor of
`(x-1)`.

The root 3 has a multiplicity of 1, and corresponds to a factor of
`(x-3)`.

So,
`f(x)=a(x+2)^2(x-1)(x-3)`.

Since
`f(0)=10`,

`10=a(0+2)^2(0-1)(0-3) \\ \\ 10=12a \\ \\ a=(5)/(6) \\ \\ \therefore f(x)=(5)/(6)(x+2)^2(x-1)(x-3)`