Question

Complete.
$z^2-2z-48=\left(z-8\right)\left(z+\square \right)$

• A. $3$
• B. $6$
• C. $12$
• D. $4$

Answer 1

The correct option is B

$6$

Step-1: The explanation for the correct option:

Option (B) :

Factoring by grouping method and simplified as follows:

$\begin{array}{rcl}{z}^2-2z-48& =& z^2-8z+6z-48\\ & \Rightarrow & z^2-2z-48=z\left(z-8\right)+6\left(z-8\right)\\ \therefore z^2-2z-48& =& \left(z-8\right)\left(z+6\right)\end{array}$

So, the missing value is $6$.

Therefore, the option $\left(B\right)$ is correct.

Step-2: Explanation for incorrect options:

Since the missing value determined above is not equivalent to the value mentioned in option $\left(A\right)$, option $\left(C\right)$, and option $\left(D\right)$.

Therefore, option $\left(A\right)$, option $\left(C\right)$, and option $\left(D\right)$ are incorrect options.

Hence, option $\left(B\right)$ is the correct answer.