Alani gives you an Algebra puzzle as follows:

Question

The expression d2 − d − 6 can be written in factored form as (d + 2)(d + k), where k represents a number. What is the value of k?

Group of answer choices

3

2

-2

-3

Answer 1

To factor the quadratic expression \( d^2 - d - 6 \), we want to express it in the form \( (d + 2)(d + k) \) and find the value of \( k \).

We can start by factoring \( d^2 - d - 6 \) by looking for two numbers that multiply to \(-6\) (the constant term) and add up to \(-1\) (the coefficient of the \(d\) term).

The factors of \(-6\) are:

• \(1\) and \(-6\)
• \(-1\) and \(6\)
• \(2\) and \(-3\)
• \(-2\) and \(3\)

Among these pairs, the numbers \(2\) and \(-3\) can be added together to give \(-1\): \[ 2 + (-3) = -1. \]

Thus, we can factor the quadratic as: \[ d^2 - d - 6 = (d + 2)(d - 3). \]

In this factored form, it is evident that \( k = -3 \).

Thus, the value of \( k \) is: \[ \boxed{-3}. \]