Chapter 14.8, Problem 7CYU

(a)

To determine

To calculate: The factors of the trinomial $x^2-5x-24$ .

Answer to Problem 7CYU

The factors for the area $x^2-5x-24{\text{ft}}^2$ are $x-8\text{and}x+3$ .

Explanation of Solution

Given Information:

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

Calculation:

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

Find the factors of the expression $x^2-5x-24$ .

Split $-5x$ into two parts such that their product is equal to the product of $x^2$ and $-24$ .

  $\begin{array}{c}{x}^2-5x-24=x^2+3x-8x-24\\ =x\left(x+3\right)-8\left(x+3\right)\\ =\left(x+3\right)\left(x-8\right)\end{array}$

Hence, the factors for the area $x^2-5x-24{\text{ft}}^2$ are $x-8\text{and}x+3$ .

(b)

To determine

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

Answer to Problem 7CYU

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.