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Harder Trinomials - Undoing FOIL

Here's another one:

Factor  7x^2 + 76x - 11

Our only choice for the first guy is

( x ) ( 7x 1 )

For the last guy, our only choice is

1 * 11

We need a middle guy of 76x.

Which one of these will work?

( x 1 ) ( 7x 11 ) ... the inner terms give 7x and the outer terms give 11x ... we cannot get a 76x using 7x and 11x ... or ... ( x 11 ) ( 7x 1 ) ... the inner terms give 77x and the outer terms give x ... 77x - x = 76x ... the inside is positive and the outside is negative

So,

7x^2 + 76x - 11 = ( x + 11 ) ( 7x - 1 )

Check it with FOIL!