Solving a quadratic inequality written in factored form Graph the solution to the following inequality on the number line. \[ (x-2)(x+4)>0 \]

To solve the inequality \((x-2)(x+4) > 0\), you'll first identify the critical points by setting each factor equal to zero: \(x - 2 = 0\) gives \(x = 2\), and \(x + 4 = 0\) gives \(x = -4\). These points divide the number line into three intervals: \((-∞, -4)\), \((-4, 2)\), and \((2, ∞)\). Choose test points from each interval - for example, \(-5\), \(0\), and \(3\) - and substitute them into the inequality. You'll find that the inequality is satisfied for intervals \((-∞, -4)\) and \((2, ∞)\). Now, when you graph the solution on a number line, represent the points \(x = -4\) and \(x = 2\) with open circles, because the inequality does not include equal to zero. Shade the regions to the left of \(-4\) and to the right of \(2\) to indicate that those intervals are included in the solution, showing that all the values satisfying the inequality are found in those ranges. Happy graphing!