Final answer:
The number of positive values for b depends on the specific prime numbers chosen as a and c in the quadratic equation.
Step-by-step explanation:
If a and c in ax² + bx + c are prime numbers and the trinomial is factorable, the discriminant (b² - 4ac) will be a perfect square. The discriminant determines the number of real roots the quadratic equation has. To find the number of positive values for b, we need to find the number of perfect square discriminants for different values of a and c.
For example, if a = 2 and c = 3, the discriminant will be 4 - 4(2)(3) = -20, which is not a perfect square. In this case, there are no positive values for b that will make the quadratic factorable.
Therefore, the number of positive values for b depends on the specific prime numbers chosen as a and c in the quadratic equation.