Chapter 4.3, Problem 39PPS

To determine

To calculate: The solution of the equation $x^2-5x-24=0$ by factoring.

Answer to Problem 39PPS

The solution of the equation is $-3\text{ and 8}$ .

Explanation of Solution

Given information:

The equation $x^2-5x-24=0$ .

Formula used:

Solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

Calculation:

Consider the given equation $x^2-5x-24=0$ .

Recall that solution of a polynomial equation is calculated using middle term splitting method and then common factors are taken out and simplified.

So, $x^2-5x-24=0$ will be factorized as,

  $\begin{array}{c}{x}^2-5x-24=0\\ x^2-8x+3x-24=0\\ x\left(x-8\right)+3\left(x-8\right)=0\\ \left(x+3\right)\left(x-8\right)=0\end{array}$ .

Therefore, either $\begin{array}{c}x+3=0\text{ or }x-8=0\\ x=-3\text{ or }x=8\end{array}$ .

Thus, the solution of the equation is $-3\text{ and 8}$ .