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2x²-12x-80
We factor out common factor 2
2(x²-6x-40)
We want to factor x²-6x-40 so we
write this:
2(x )(x )
First we look at the 40
(We work right to left on the x²-6x-40)
Ww write down all the ways two whole numbers
can be multiplied to give 40, they are
40·1
20·2
10·4
8·5
We look at x²-6x-40 for the sign of the 40.
It is - so out beside those we SUBTRACT
those numbers: [If it were + we would ADD here]
40·1 40-1 = 39
20·2 20-2 = 18
10·4 10-4 = 6
8·5 8-5 = 3
Next we look at x²-6x-40 for the 6 and we see that 6
is listed among those subtractions. So we use the
10 and the 4.
We write the 10 in the first parentheses and the 4 in
the second
2(x 10)(x 4)
Next we look at x²-6x-40 for the sign of the 6. It
is -, so we put a - next the larger number 10:
2(x-10)(x 4)
Finally we look back at the sign of 40. It is -,
so the sign of the 4 must be OPPOSITE to the sign
in the first parentheses, so it must be +:
2(x-10)(x+4)
[If the sign of 40 had been + we would have put
the SAME sign]
Edwin
