The expression `a^{2}+11a+24` can be written in factored form as `\left(a+8\right)\left(a\ +\ k\right)`, where `k` represents a number. What is the value of `k`?
To find the value of k, we need to factor the expression a^2 + 11a + 24.
To factor this expression, we need to find two numbers that multiply to 24 (the coefficient of the constant term) and add up to 11 (the coefficient of the middle term).
The numbers that fit these criteria are 8 and 3. 8 * 3 = 24 and 8 + 3 = 11.
Therefore, we can rewrite the expression as:
a^2 + 11a + 24 = (a + 8)(a + 3)
Therefore, the value of k is 3.