Chapter 9.2, Problem 49CCR

To determine

To write:an expression in factored form to represent the total area for each figure

Answer to Problem 49CCR

The expression $7\left(x+8\right)$ in factored form

Explanation of Solution

Given information:

  

Calculation:

The total area for each figure

  $\begin{array}{l}2x+5x+56\\ =7x+56\end{array}$

The greatest common factor

  $\begin{array}{l}7x=7\cdot x\\ 56=2\cdot 2\cdot 2\cdot 7\end{array}$

Therefore, the greatest common factor is 7.

  $\begin{array}{l}7x+56\\ =\left(7\cdot x+2\cdot 2\cdot 2\cdot 7\right)\\ =7\left(x+8\right)\end{array}$

Therefore, the greatest common factor is 7.

Hence, the expression $7\left(x+8\right)$ in factored form.