Factoring and Solving a Quadratic with Leading Coefficient of 1

To factor $x^2+x-6=0,$ we look for two numbers whose product equals $\mathrm{-6}$ and whose sum equals 1. Begin by looking at the possible factors of $\mathrm{-6.}$

The last pair, $3\cdot \left(\mathrm{-2}\right)$ sums to 1, so these are the numbers. Note that only one pair of numbers will work. Then, write the factors.

To solve this equation, we use the zero-product property. Set each factor equal to zero and solve.

The two solutions are $2$ and $\mathrm{-3.}$ We can see how the solutions relate to the graph in Figure 2. The solutions are the x-intercepts of $y=x^2+x-6=0.$