Find the solution set for x^2 -4x -5 > 0.

• A. x < -1
• B. -1 < x < 5
• C. x > 5
• D. x < -1 or x > 5

Answer: (D)

This asks where the quadratic sits above the x-axis. Start by factoring: x^2 - 4x - 5 = (x - 5)(x + 1). The product is positive when the two factors have the same sign, which happens on intervals determined by the zeros at -1 and 5. Testing each interval helps: pick x = -2 (gives positive), x = 0 (gives negative), and x = 6 (gives positive). Since we want strictly greater than zero, the points where the expression equals zero (-1 and 5) aren’t included. So the solution is x < -1 or x > 5.