Chapter 8, Problem 5GR

Solution

To find:Thefactor of the expression.

  $\left(x-2\right)$ and $\left(x+3\right)$ .

Given Information:

  $x^2+x-6$

Calculation:

  $\begin{array}{l}\Rightarrow x^2+x-6\\ \Rightarrow \left(x^2-2x\right)+\left(3x-6\right)\\ \Rightarrow x\left(x-2\right)+\left(3x-6\right)\left[\text{factor out }x\right]\\ \Rightarrow x\left(x-2\right)+3\left(x-2\right)\left[\text{factor out 3}\right]\\ \Rightarrow \left(x-2\right)\left(x+3\right)\left[\text{factor out common term}\right]\end{array}$

Thus,the solutions are $\left(x-2\right)$ and $\left(x+3\right)$ .