How do u find the lcf

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.