n^2-n-30
using the foil method, explain your work
To factor the expression n^2 - n - 30 using the FOIL method, we need to find two numbers that multiply to -30 and add up to -1 (the coefficient of the n term).
Let's list the factors of -30:
1, -30
-1, 30
2, -15
-2, 15
3, -10
-3, 10
5, -6
-5, 6
Among these factors, the pair that adds up to -1 is 5 and -6.
Therefore, we can rewrite the expression as:
n^2 - n - 30 = n^2 + 5n - 6n - 30
Now, we can factor out common terms:
= n(n + 5) - 6(n + 5)
Finally, we can factor out the common binomial factor (n + 5) to obtain the final factored form:
= (n - 6)(n + 5)