Chapter 8.5, Problem 8STP

The area of a rectangular backyard is given by the trinomial $b^2+5b-24.$

What are possible dimensions of the backyard? Show why your answer is correct.

To determine

To find: Dimension of the rectangular backyard.

Answer to Problem 8STP

Dimension of the backyard are $\left(b-3\right)$ and $\left(b+8\right)$ .

Explanation of Solution

Given information: area of rectangular backyard is given by trinomial $b^2+5b-24$

To find the dimension of the backyard find the factor of given quadratic expression,

  $\begin{array}{l}{b}^2+8b-3b-24\\ b\left(b+8\right)-3\left(b+8\right)\\ \left(b-3\right)\left(b+8\right)\end{array}$

Therefore dimension of the backyard are $\left(b-3\right)$ and $\left(b+8\right)$ .

To proof the answer multiply the both factor,

  $\begin{array}{l}\left(b-3\right)\left(b+8\right)\\ b^2+8b-3b-24\\ b^2+5b-24\end{array}$

Therefore this is the required answer.