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Factor completely using trial and error method: 6x^2+23x+15
GCF=1
115 35 53 151
first term not just x
means either: (2x ) ( 3x ) or (x )(6x )
(2x + 1 ) ( 3x + 15)
3x
30x
3x + 30x != 23x
2nd binomial has gcf of 3 but gcf in trinomial is 1 if there was no gcf to remove in original trinomial, why would there be one after factoring?
this means we can remove 5 and 3 from list of things to go through, in addition to 1 and 15, as they would create that GCF 3 situation again
(2x + 3 ) ( 3x + 5 )
9x
10x
9x+10x != 23x
(2x + 15 ) ( 3x + 1 )
45x
2x
45x+2x!=23x
(x) (6x)
1 and 15 cant work 5 and 3 cant work this is because if you put 15 or 3 in second parenthese, you get a GCF of 3 instead of 1
(x+3) (6x+5)
18x
5x
18x+5x=23x
(x+3)(6x+5)=6x^2+5x+18x+15 6x^2+23x+15