find all the possible values of b such that 3x^2 + bx -2 can be factored

Given the quadratic equation:

3x^2 + bx - 2

Determine all the possible values whereas the quadratic function can be factored.

Explanation:

Since it is not given in the condition whether the value of b is positive, or negative, and it is not also stated whether the value of b should make the quadratic equation a perfect square equation, therefore we can simply put any values of b. This can be represented by either using interval notation, or through foster method. Hence, we can put any values of by, such that it can be factored by using the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

Conditions of the quadratic formula:
When b^2−4ac=0 there is one real root.
When b^2−4ac>0 there are two real roots.
When b^2−4ac<0 there are no real roots, only a complex number.

In our case we do not have to worry about having no real roots or complex numbers, since we have a negative value of c, which means that b^2 - 4ac, will become b^2 + 4ac.

Final answer:

{ -∞, +∞ )