Posted by **Diana** on Saturday, February 11, 2012 at 4:06pm.

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

- algebra -
**Steve**, Saturday, February 11, 2012 at 6:18pm
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^2-5x+2 = (3x-2)(x-1)

3x^2+5x+2 = (3x+2)(x+1)

3x^2-7x+2 = (3x-1)(x-2)

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.

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