Final answer:
A value of c that makes the discriminant of the quadratic 3x^2 + 5x + c non-perfect square results in the expression being non-factorable. For example, c=3 would result in a discriminant of -11, which is not a perfect square, therefore the quadratic would be non-factorable.
Step-by-step explanation:
The question is asking us to find a value of c that would result in the quadratic expression 3x^2 + 5x + c being non-factorable. To determine this, we use the discriminant in the quadratic formula, which is b^2 - 4ac. For a quadratic to be factorable over the integers, the discriminant needs to be a perfect square.
In this case, our equation is 5^2 - 4 × 3 × c. The quadratic will be non-factorable if the discriminant is not a perfect square. Thus, we must find a value of c such that 25 - 12c is not a perfect square.
For example, if c=2, then 25 - 12 × 2 gives us 1, which is a perfect square, meaning the quadratic is factorable. However, if c=3, the discriminant would be 25 - 12 × 3 = -11, which is not a perfect square, and thus the quadratic would be non-factorable.