Posted by Diana on .
Find all integers b so that the trinomial 3x^2 +bx + 2 can be factored.

algebra 
Steve,
The discriminant must be positive for there to be real roots, that is, factors
so, b^2  24 > 0
b must be an integer such that b >= 5
3x^25x+2 = (3x2)(x1)
3x^2+5x+2 = (3x+2)(x+1)
3x^27x+2 = (3x1)(x2)
3x^2+7x+2 = (3x+1)(x+2)
Many others are possible, not all of which factor into rational roots. Any integer b > 5 will provide real roots, however.