[tex] \\p(x) = a {x}^{3} + b {x}^{2} + cx + 12 \\ \\ a .{1}^{3} + b. {1}^{2} +c.1 + 12 = 1 \\ a + b + c + 12 = 1 \\ a + b + c = - 11 \\ \\ a. {2}^{3} + b. {2}^{2} + c.2 + 12 = 4 \\ 8a + 4b + 2c + 12 = 4 \\ 8a + 4b + 2c = - 8 \\ 4a + 2b + c = - 4 \\ \\ a. {3}^{3} + b. {3}^{2} + c.3 + 12 = 9 \\ 27a + 9b + 3c + 12 = 9 \\ 27a + 9b + 3c = - 3 \\ 9a + 3b + c = - 1 \\ \\ - a - b - c = 11 \\ 4a + 2b + c = - 4 \\ + - - - - - - - - - - \\ 3a + b = 7 \\ \\ - 4a - 2b - c = 4 \\ \: 9a + 3b + c = - 1 \\ + - - - - - - - - - - - \\ 5a + b = 3 \\ \\ - 3a - b = - 7 \\ 5a + b = 3 \\ + - - - - - - - \\ 2a = - 4 \\ a = - 2 \\ b = 13 \\ c = - 22 \\ \\ \\ p(x) = - 2 {x}^{3} + 13 {x}^{2} - 22x + 12 \\ p(4) = 2. {4}^{3} + 13. {4}^{2} - 22.4 + 12 \\ p(4) = 2.64 + 13.16 - 22.4 + 12 \\ p(4) =128 + 208 - 88 + 12 = 260 [/tex]