Question

question
factor.
$x^2 - x - 72$

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(-72\) and add up to \(-1\). Let's list the factor pairs of \(72\): \((1, 72)\), \((2, 36)\), \((3, 24)\), \((4, 18)\), \((6, 12)\), \((8, 9)\). We need one positive and one negative number since their product is negative. The pair \(8\) and \(-9\) works because \(8\times(-9)= -72\) and \(8 + (-9)= -1\).

Step2: Factor the quadratic

Using the numbers we found, we can factor \(x^{2}-x - 72\) as \((x + 8)(x - 9)\) because when we expand \((x + 8)(x - 9)\), we get \(x^{2}-9x + 8x - 72=x^{2}-x - 72\).

Answer:

\((x + 8)(x - 9)\)