Answer:
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
