Can someone help me factor this 5x^2+8x+9

Question

What's the technique in factoring

Answer 1

just a lot of experience, some guesses, and some luck. You know from looking at it that the factors will be of the form

(5x+a)(x+b)
where the two a,b are one each of 1,9.

You need 5b+9a = 8

Now, even a cursory look assures you that there are no such a,b both positive where this can be the case.

A quick check of the discriminant shows that it is 8^2-4*9*5 = 64-180 < 0, so there are no real roots. That means no factors over the rationals.

Is there a typo here? The beast can certainly not be factored.