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- Apr 13, 2013

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The interpolating polynomial that interpolates at the following data:

$f(5)=?,f(8)=14,f(12)=214$ is $4,125x^{2}-32,5x+10$.

The corresponding interpolating polynomial in the Newton form is $p_{2}(x)=a_{0}+a_{1}(x-5)+a_{2}(x-5)(x-3)$.Which is the value of $a_{2}$?

Is it 4,125 because the two polynomials should be equal or am I wrong?