Question
Alani gives you an Algebra puzzle as follows:
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
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
Answers
GPT-4o mini
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:
\[
\boxed{-3}.
\]
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:
\[
\boxed{-3}.
\]