Factor the numerator: x⁴ − 5x² + 4 = (x² − 1)(x² − 4) = (x − 1)(x + 1)(x − 2)(x + 2). For x ≠ 1, 2, f(x) = (x + 1)(x + 2). At x = 1, this gives 6, matching the defined value. At x = 2, it gives 12, again matching the defined value. Hence the function is continuous for every real number.
