How do you factor 2x^2-5x+2?

Question

(x-2)(2x-1)

how do you figure that out?

trinomials like that can usually be done intuitively, but you should have been taught a method that you can use for general cases.

Look at the first term of 2x^2 and think where that can come from?
(x...)(2x...) is the only possibility.

Now look at the last term of +2
your brackets must have ended with +1 and +2 or -1 and -2
but surely they had to be both negative since the middle term is negative.

so now your choices are
(x-1()2x-2) or (x-2)(2x-1)

mentally expand them, only one gives you the correct middle term of the original.

So there is no way to incorporate the middle term from the beginning, like when there is no number in front of the x^2? And the only way to do it is keep guessing and checking?