Construct a polynomial function of least degree possible using the given information.

Real roots: - 2, 1/2 (with multiplicity 2) and (-3, f (-3)) = (-3,5)

Theorem: If a function y = f (x) has a real root of b, then (x - b) is a factor of f (x).

As given in the problem, there are two roots: - 2 and 1/2. The multiplicity of 1/2 is 2 meaning that the root 1/2 repeats twice. So the function f (x) can be written like this.

f (x) = k• (x - (-2)) (x - 1/2) ^2 = k• (x + 2) (x - 1/2) ^2

We're supposed to find the coefficient k to complete the function.

Given that f (-3) = 5, we can plug - 3 in for x and 5 in for f (x).

So 5 = k • (-3 + 2) (-3 - 1/2) ^2

5 = k (-1) (-7/2) ^2

5 = - k•49/4

Then 5 • 4/49 = - k

Or k = - 20/49

So the function with the least degree is

f (x) = - 20/49 (x + 2) (x - 1/2) ^2.