## Algebra 1: Common Core (15th Edition)

The possible dimensions of the rectangle are $x+8$ and $x-9$.
To factor $x^{2}-x-72$, identify the pair of factors of $-72$ that has a sum of $-1$. $\left[\begin{array}{lll} \text{Factors of -72 } & \text{Sum of factors} & \\ 1\text{ and }-72 & -71 & \\ -1\text{ and }72 & 71 & \\ 2\text{ and }-36 & -34 & \\ -2\text{ and }36 & 34 & \\ 3\text{ and }-24 & -21 & \\ -3\text{ and }24 & 21 & \\ 4\text{ and }-18 & -14 & \\ -4\text{ and }18 & 14 & \\ 6\text{ and }-12 & -6 & \\ -6\text{ and }12 & 6 & \\ 8\text{ and }-9 & -1 & \text{...is what we need} \end{array}\right]$ $x^{2}-x-72=(x+8)(x-9)$ The possible dimensions of the rectangle are $x+8$ and $x-9$.