Final answer:
The value of c that would not make the quadratic equation 3x^2 + 5x + c factorable is c = 22, because it results in a negative discriminant, indicating that the quadratic equation has complex solutions.
Step-by-step explanation:
To determine which value of c would not make the quadratic equation 3x^2 + 5x + c factorable, we can use the discriminant method from the quadratic formula. The discriminant is found by using b^2 - 4ac. A quadratic equation is factorable over the real numbers if and only if the discriminant is a perfect square (which means the quadratic formula will produce rational solutions).
In this case, a = 3 and b = 5.
The discriminant for the equation 3x^2 + 5x + c is 5^2 - 4(3)(c), which simplifies to 25 - 12c. To determine which provided values of c would result in a non-factorable quadratic, we need the discriminant to be a non-perfect square or a negative number (indicating complex solutions).
- For c = 2, the discriminant is 25 - 12(2) = 1, which is a perfect square.
- For c = -2, the discriminant is 25 - 12(-2) = 49, which is also a perfect square.
- For c = 22, the discriminant is 25 - 12(22) = -239, which is negative, thus non-factorable over real numbers.
- For c = -22, the discriminant is 25 - 12(-22) = 289, which is a perfect square.
Therefore, c = 22 is the value that would not make the quadratic equation factorable.