Question

Factor the expression:
$n^2-15n+56$

• A. $\left(n+7\right)\left(n+8\right)$
• B. $\left(n+7\right)\left(n-8\right)$
• C. $\left(n-7\right)\left(n-8\right)$
• D. $\left(n-7\right)\left(n+8\right)$

Answer 1

The correct option is C

$\left(n-7\right)\left(n-8\right)$

Step-1: Explanation for correct option:

Option (C) :

Factoring by grouping method and simplified as follows:

$\begin{array}{rcl}{n}^2-15n+56& =& n^2-8n-7n+16\\ & \Rightarrow & n^2-15n+56=n\left(n-8\right)-7\left(n-8\right)\\ \therefore n^2-15n+56& =& \left(n-8\right)\left(n-7\right)\end{array}$

So, the factor is $\left(n-7\right)\left(n-8\right)$.

Therefore, this option 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 $\left(B\right)$, and option $\left(D\right)$.

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

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