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Trinomials - Undoing FOIL

Now, look at the last term of our trinomial: - 45

x^2 - 4x - 45 ... -4x is the middle term and -45 is the last term

and our middle coefficient: -4

All we need to do is figure out what signs to put in this

( x 5 ) ( x 9 )

to give BOTH the -45 and the -4...

It can't be

( x + 5 ) ( x + 9 )

because this would give us a POSITIVE 45.

For the same reason, it can't be

( x - 5 ) ( x - 9 )

We need to use a + and a - ...

and we need a -4 ...

+5 - 9 = -4 and ( +5 ) ( -9 ) = -45

So,    x^2 - 4x - 45 = ( x - 5 ) ( x - 9 )

Check it with FOIL!