Posted by Julie on Wednesday, January 23, 2013 at 4:17pm.
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.
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