k^2+13k+42
using the foil method, explain your work
To factor the expression k^2 + 13k + 42 using the foil method, we need to find two numbers that multiply to 42 and add up to 13.
First, let's list the factors of 42:
1, 2, 3, 6, 7, 14, 21, 42
Now, let's check which pair of factors add up to 13:
7 + 6 = 13
Therefore, we can rewrite the expression as:
k^2 + 13k + 42 = k^2 + 7k + 6k + 42
Now we can factor by grouping:
k(k + 7) + 6(k + 7)
Notice that we have a common factor of (k+7) in both terms, so we can factor it out:
(k + 7)(k + 6)
Therefore, the factored form of k^2 + 13k + 42 using the foil method is (k + 7)(k + 6).