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Trinomials - Undoing FOIL

TRY IT:

Factor  x^2 - x - 20 = ( x 4 ) ( x 5 )
Factor   a^2 - 5a - 24 = ( a 3 ) ( a 8 )

Now, I'll take a crutch away...

Let's factor  x^2 - 4x - 12

I'll give you

( x 2 ) ( x ) ... we need the second number and the signs

What goes in here?

( 2 ) ( ? ) = 12 ... the unknown is 6, therefore we can now write ( x 2 ) ( x 6 )

What about the signs?

The last term is -12.

The middle coefficient is -4.

Since the last term is negative, we need a  +  and a  -

Which is it?