Finite Difference

Algebra Level 4

Let P(x) be a cubic polynomial of the form \(a{ x }^{ 3 }+b{ x }^{ 2 }+cx+d\)

IF: P(1) = 12 P(2) = 44 P(3) = 140 P(4) = 330

Then what does P(5) equal?

Hint: making a triangle of differences may help

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