If P (x) = ax^4 + bx^3 + cx^2 + dx + e has roots at x = 1, 2, 3, 4 and P (0) = 48.

Determine the value of P (5).

If P (x) = ax^4 + bx^3 + cx^2 + dx + e has roots at x = 1, 2, 3, 4, then

0 = a + b + c + d + e0 = 16 a + 8b + 4c + 2d + e0 = 81 a + 27b + 9c + 3d + e0 = 256 a + 64 b + 16c + 4d + e

P (0) = 48 e = 48

There are five equations, five unknowns, hence the linear equations can be solved. a is equal to 2, b is equal to - 20, c is equal to 70, d is equal to - 100 and e is equal to 48