Chapter 14.8, Problem 18PPS

(a)

To determine

To calculate: The factors of the trinomial $l^2-5l-6$ .

Answer to Problem 18PPS

The factors for the area $l^2-5l-6\text{square}\text{inches}$ are $l+1\text{and}l-6$ .

Explanation of Solution

Given Information:

  $\text{Area}=l^2-5l-6\text{square}\text{inches}$

Calculation:

The given area is $l^2-5l-6\text{square}\text{inches}$ .

Find the factors of the expression $l^2-5l-6$ .

Split $-5l$ into two parts such that their product is equal to the product of $l^2$ and $-6$ .

  $\begin{array}{c}{l}^2-5l-6=l^2-6l+l-6\\ =l\left(l-6\right)+1\left(l-6\right)\\ =\left(l+1\right)\left(l-6\right)\end{array}$

Hence, the factors for the area $l^2-5l-6\text{square}\text{inches}$ are $l+1\text{and}l-6$ .

(b)

To determine

To calculate: The area for the trinomial $x^2-5x-24$ when $x=10$ .

Answer to Problem 18PPS

The area is 26 square feet.

Explanation of Solution

Given Information:

  $\text{Area}=x^2-5x-24{\text{ft}}^2$

  $x=10$

Calculation:

The given area is $x^2-5x-24{\text{ft}}^2$ .

Find the area when $x=10$ .

Substitute 10 for $x$ in the expression $x^2-5x-24$ .

  $\begin{array}{c}\text{Area}=x^2-5x-24\\ ={10}^2-5\times 10-24\\ =100-50-24\\ =26\end{array}$

Hence, the area is 26 square feet.