(5x-2)(x-3).
How to do it? Factors of 5 are 5 and 1 so we have (5x...)(x...) to start with.
The sign of the constant is + so we have (5x-...)(x-...) or (5x+...)(x+...). The sign of the x term tells us that it must be minus in both.
Factors of 6 are 1 and 6 or 2 and 3. The coefficient of the middle term is 17 so we are looking at which factors of 6 satisfy. Here are all the possibilities (the + is the same sign as the constant +6):
- 5*1+1*6=11
- 5*6+1*1=31
- 5*2+1*3=13
- 5*3+1*2=17
The last one gives us what we want. That means 3 goes in the other bracket to the one containing 5:
(5x-2)(x-3)