The expression n^2 + n - 20 can be written in factored form as (n - 4) (n + k), where k represents a number. what is the value of k?
To factor the expression n^2 + n - 20, we need to find two numbers that multiply to give -20 and add to give 1 (the coefficient of n). These two numbers are 5 and -4, because 5 * (-4) = -20 and 5 + (-4) = 1.
Therefore, we can write n^2 + n - 20 as (n + 5)(n - 4).
Comparing this to the given expression (n - 4) (n + k), we see that k must be 5, because the second factor in both expressions is n + 5.
Therefore, the value of k is 5.
To find the value of k, we need to factor the expression n^2 + n - 20.
Step 1: We need to find two numbers that multiply to -20 and add up to 1 (since the coefficient of n is 1).
The numbers that fulfill these conditions are 5 and -4, since 5 * -4 = -20 and 5 + (-4) = 1.
Step 2: Now we can write the expression in factored form.
n^2 + n - 20 = (n + 5)(n - 4)
So, k = 5.