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

Real roots: - 1, 1, 3 and (2,

f (2)) = (2, 5)

f (x) = (-5/3) x³ + 5x² + (5/3) x - 5

Step-by-step explanation:

For root "a", the polynomial will have a factor (x - a). Given the three roots, the polynomial will be the product of the three factors ...

... p (x) = (x + 1) (x - 1) (x - 3)

The value of p (2) is 3·1· (-1) = - 3. In order to make f (2) = 5, we need to multiply p (x) by - 5/3.

... f (x) = (-5/3) p (x)

... f (x) = (-5/3) (x + 1) (x - 1) (x - 3)

Expanding gives

... f (x) = (-5/3) x³ + 5x² + (5/3) x - 5