15x² - 108x + 108
This is what I would do.
First take out common factors I mean take out the 3
\(=3(5x^2-36x+36)\)
Now I want two numbers that multiply to be 5*36=180
Since the multiple of 5 and 36 is positive the two numbers must both be positive OR both be negative.
The numbers need to add to -36 (the middle one) so they must both be negative.
Here I do use a bit of trial and error
5*36=5*2*3*2*3 = 5*6*6 = 30*6 bingo the numbers are -30 and -6
-30*-6=180
-30+-6=-36
\(=3(5x-30x-6x+36)\)
Anyway, I hope that helps ;)
Another way to do it is to utilize the quadratic formula from that you can just gives the final factors not the break down of it.
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