Suppose $P(x) = ax^4 + bx^3 + cx^2 + dx + e$ satisfies $P(1) = 1, P(2) = 2, P(3) = 3, P(4) = 4$,

Question

Suppose $P(x) = ax^4 + bx^3 + cx^2 + dx + e$ satisfies $P(1) = 1, P(2) = 2, P(3) = 3, P(4) = 4$, it is also given $P(5) = -19$. Find $P(6)$.

Accepted Answer

$-114$.

Polynomials, Cubic Equations and Partial Fractions