Question

Name the values of b which make the expression x^2 − 3x + b factorable.

Answer 1

the discriminant is 9-4b
if by factorable you mean using rational numbers, then 9-4b must be a perfect square.
so, b=2 or -4
x^2-3x+2 = (x-1)(x-2)
x^2-3x-4 = (x+1)(x-4)

or, using the fact the the two roots p and q must satisfy
pq = b
p+q = 3
so since the only rational roots are ±b then p = ±1, making
q = 2 or 4
for the solutions named above