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Solve for real x: x(x + 1)(x + 2)(x + 3) = 24.

1. x = 1 or x = -4
2. x = 1 or x = 4
3. x = -1 or x = 4
4. x = 2 or x = -3

Correct answer: x = 1 or x = -4

Solution

Group: x(x+3) = x² + 3x and (x+1)(x+2) = x² + 3x + 2. Let y = x² + 3x: y(y+2) = 24 => y² + 2y - 24 = 0 => (y+6)(y-4) = 0 => y = 4 or y = -6. y = x² + 3x = 4 => x² + 3x - 4 = 0 => x = 1 or x = -4 (real). y = -6 => x² + 3x + 6 = 0 has no real roots (discriminant 9 - 24 < 0). Real solutions: x = 1, x = -4.

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