For the next two (02) items that follow: x⁴ + px³ + qx² + x + 6 is divisible by x² - x - 6. What is the value of p?

x² - x - 6 = (x - 3)(x + 2). Since the polynomial is divisible by x² - x - 6, both x = 3 and x = -2 are roots. Substituting x = 3: 81 + 27p + 9q + 3 + 6 = 0, so 27p + 9q = -90, i.e., 3p + q = -10. Substituting x = -2: 16 - 8p + 4q - 2 + 6 = 0, so -8p + 4q = -20, i.e., -2p + q = -5. Subtracting: 5p = -5, so p = -1.