Thread: Construct a polynomial function passing through a point

I am stuck at this problem, anyone have any ideas where I would start?

Construct a polynomial function with these stated properties (reduce all fractions):

Third-degree, with zeros of -3, -1, and 2, and passes through the point (4,10).

Thank you for any help!

This is pretty easy, because know 3 zeros of a function (3rd degree)

thats why this function has the form

f(x) = a*(x + 3)*(x + 1)*(x - 2)


now u have to find the a

f(4) = a*(4+7)(4+1)(4-2) = 70a = 10

=> a = 1/7

=> f(x) =1/7(x + 3)*(x + 1)*(x - 2)