x² + 6x - 16
Think of two integers which multiply to give 16 yet subtract to give 6
They are 8 and 2, because 8×2 = 16 and 8-2=6, so write this first without
signs:
(x 8)(x 2)
Then to make the 8 and the 2 multiply to give the last term of the
original-16, you have to give one of them a + sign and the other a
- sign. So it's either
(x - 8)(x + 2) or (x + 8)(x - 2)
FOIL them both out and you'll see that the first one gives x² - 6x - 16,
which is not the original, but when you FOIL out the second one you get
x² + 6x - 16, which is the original.
So the answer is
(x + 8)(x - 2)
Edwin
