Construct a polynomial function of least degree possible

Question

Construct a polynomial function of least degree possible using the given information.
Real roots: −4, −1, 1, 4 and (−2,
f(−2)) = (−2, 17)
f(x) =

 

I know most of the function I just can't figure out how to get the fraction in the front.

-fraction? (x^4-17x^+16)

Answer 1

f(x) = C(x² - 1)(x² - 16)

f(x) = C(x⁴ - 17x² + 16)

 

Solve for C when    x=-2   and     f(x)=17