How do I factorise quickly instead of using trial and error?

F

Flipper

New member
Is there a way to figure out how to factorise something without testing all possible answers?
I have to factorise 28x^2 - 19x - 20. I can do it but it's going to take me ages if I have to test all the multiples of 28 and 20. Is there a faster way or will I just have to get used to it?
I don't need to work out the answer, I just need to factorise it.
 
28x? - 19x = 20
x? - 19/56x = 5/7 + (- 19/56)?
x? - 19/56x = (2,240 + 361)/3,136
(x - 19/56)? = 2,601/3,136
x - 19/56 = ? 51/56

= x - 19/56 - 51/56, = x - 70/56, = x - 5/4, = 4x - 5
= x - 19/56 + 51/56, = x + 32/56, = x + 4/7, = 7x + 4

Answer: (4x - 5)(7x + 4)
 
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