Construct a polynomial function with the stated properties

Question

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

Answer 1

Try constructing a function from a product of factors containing the zeros, with an unknown coefficient:

 

f(x) = a [x - (-2)] [x - (-1)] (x - 3)

 

with a ≠ 0.

 

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

 

Use f(4) = 10 to find a.

 

10 = a(4 + 2)(4 + 1)(4 - 3) = 30a

 

a = 1/3

 

f(x) = (1/3)(x + 2)(x + 1)(x - 3)

 

Expand this into polynomial form and you are done.  Can you finish from here?