x^2-14x-72
using the foil method, explain your work
To factor the expression x^2-14x-72 using the FOIL method, we need to find two numbers that multiply to -72 and add up to -14.
1. First, we identify the coefficient of x^2, which is 1. This means our factors will be in the form of (x +/- a)(x +/- b), where a and b are the two numbers we need to find.
2. Next, we list all possible factor pairs of -72:
-1, 72
-2, 36
-3, 24
-4, 18
-6, 12
3. Some trial and error leads us to the correct pair: -18 and 4.
-18 * 4 = -72
-18 + 4 = -14
4. Now we can rewrite the expression with the factors we found:
x^2 - 18x + 4x - 72
5. Next, factor by grouping:
x(x - 18) + 4(x - 18)
6. Factor out the common factor, (x - 18):
(x + 4)(x - 18)
So, x^2 - 14x - 72 can be factored as (x + 4)(x - 18) using the FOIL method.