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Harder Trinomials - Undoing FOIL

First terms: 1 * 8 and 2 * 4 , Last terms: 1 * 9 and 9 * 1 and 3 * 3


Our middle guy is -6w
 

1) 1 * 8 and 1 * 9 gives 8 and 9 ... no

2) 1 * 8 and 9 * 1 gives 72 and 1 ... no

3) 1 * 8 and 3 * 3 gives 24 and 3 ... no

4) 2 * 4 and 1 * 9 gives 4 and 18 ... no

5) 2 * 4 and 9 * 1 gives 36 and 2 ... no

6) 2 * 4 and 3 * 3 gives 12 and 6 ... -12 + 6 = -6

First: 2 * 4 and Last: 3 * 3 gives ( 2w - 3 ) ( 4w + 3 ) ... the inner terms give -12w and the outer terms give 6w

So,

8w^2 - 6w - 9 = ( 2w - 3 ) ( 4w + 3 )

Check with FOIL!