Chapter 8.8, Problem 29PPE

To determine

To find:the expression for dimension of rectangular prism.

Answer to Problem 29PPE

The expression for dimension of rectangular prism is $4c\left[\left(c+5\right)\left(c+8\right)\right]$ .

Explanation of Solution

Given info:

The volume of the rectangular prism is $V=4c^3+52c^2+160c$

Formula used:

Show the general form of trinomial as follows:

  $a{x}^2+bx+c$

Here, $a,b,c$ are integers, $b$ is the value which depends on the multipliers $\left(n,m\right)$ of the product of $a$ and $c$ .

Show the factorization of trinomial form as follows:

  $\begin{array}{l}a{x}^2+bx+c\\ a{x}^2+nx+mx+c\\ x\left(ax+n\right)+\left(mx+c\right)\end{array}$

Calculation:

Find the dimension of the rectangular prism by factorization rule as follows:

  $\begin{array}{l}=4c^3+52c^2+160c\\ =4c\left[\left(c^2+13c+40\right)\right]\\ =4c\left[\left(c^2+8c+5c+40\right)\right]\\ =4c\left[c\left(\left(c+8\right)+5\left(c+8\right)\right)\right]\\ =4c\left[\left(c+5\right)\left(c+8\right)\right]\end{array}$

Hence, the expression for dimension of rectangular prism is $4c\left[\left(c+5\right)\left(c+8\right)\right]$

Conclusion:

Thus, the expression for dimension of rectangular prism is $4c\left[\left(c+5\right)\left(c+8\right)\right]$