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Harder Trinomials - Undoing FOIL

Check this out:

Factor  15x^2 + 7x + 4


First terms: 1 * 15 and 3 * 5 , Last terms: 1 * 4 and 4 * 1 and 2 * 2

We need a 7x.
 

1) 1 * 15 and 1 * 4 gives 15 and 4 ... no

2) 1 * 15 and 4 * 1 gives 60 and 1 ... no

3) 1 * 15 and 2 * 2 gives 30 and 2 ... no

4) 3 * 5 and 1 * 4 gives 5 and 12 ... -5 + 12 = 7

First: 3 * 5 and Last: 1 * 4 gives ( 3x - 1 ) ( 5x + 4) ... the inner terms give -5x and the outer terms give 12x


Check with FOIL:		 ( 3x - 1) ( 5x + 4 ) = 15x^2 + 7x - 4 ... NO!

Dead end -- keep going!

5) 3 * 5 and 4 * 1 gives 20 and 3 ... no

6) 3 * 5 and 2 * 2 gives 10 and 6 ... NO!

That's it! All possibilities have been exhausted. No sweating on the test --I'm sure!

This thang doesn't factor, Baby!

YOUR TURN:

PROVE that  7x^2 - 33x + 10  does NOT factor.