Step-by-step answer:
The fastest way is to factor the given expression, either by inspection or grouping.
We write
3x^2+10x+3 ..........................................(1)
= (3x^2+x)+9x+3
= x(3x+1) + 3(x+1)
=(x+3)(3x+1)
so (3x+1) is a factor.
We can also eliminate the two other factors by observing
(3x+3) = 3(x+1), but 3 is not a common factor in (1), so this can be eliminated.
(3x-1) has a negative sign, but (1) does not have ANY negative sign, so again this can be eliminated. That leaves (3x+1) as the only possibility. Again, factoring confirms that it is.