Malcolm has been watching a roulette-style game at a local charity bazaar. The game has only ten numbers on the wheel, and every
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Given a polynomial and a point
, we have that
We know that our cubic function is zero at -4, 0 and 5, which means that our polynomial is a multiple of
Since this is already a cubic polynomial (it's the product of 3 polynomials with degree one), we can only adjust a multiplicative factor: our function must be
To fix the correct value for a, we impose :
And so we must impose
So, the function we're looking for is