Question

question 4 20 pts the expression ( d^2 - d - 6 ) can be written in factored form as ( (d + 2)(d + k) ), where ( k ) represents a number. what is the value of ( k )?

Explanation:

Step1: Expand the factored form

$(d+2)(d+k) = d^2 + kd + 2d + 2k = d^2 + (k+2)d + 2k$

Step2: Equate coefficients with original

Original: $d^2 - d - 6$. Match constant terms:
$2k = -6$

Step3: Solve for k

$k = \frac{-6}{2} = -3$
Verify linear term: $k+2 = -3+2 = -1$, which matches the coefficient of $d$ in the original expression.

Answer:

$-3$