Since all the signs are positive you know that if this expression can be factored the factors will be
10x2 + 17x + 6 = (px + q)(rx + s)
where p, q, r and s are positive integers.
p and r must be factors of 10 so they can be 1, 2, 5 or 10.
q and s must be factors of 6 so they can be 1, 2, 3 or 6.
This gives 16 possibilities (not very many) so try them until you find one that works or you conclude that the expression can't be factored. I'll get you started.
Suppose p = 1 then r = 10 so you have
(x + q)(10x + s)
q = 1 so s = 6: (x + 1)(10x + 6): middle term is 16 x: doesn't work
q = 2 so s = 3: (x + 2)(10x + 3): middle term is 23 x: doesn't work
try q = 3 and q = 6 and so on.
If none of these give a factorization go to p = 2 and then r = 5 and try the various choices for q. If none of these work try p = 5 and continue.
I hope this helps,