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  3. suppose f is a degree n polynomial where f(a1) = b

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2, · ·...

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Advance Math

Suppose f is a degree n polynomial where f(a1) = b1, f(a2) = b2,· · · f(an+1) = bn+1 where a1, a2, · · · an+1 are n + 1 distinctvalues. We will define a new polynomial g(x) = b1(x − a2)(x − a3)·· ·(x − an+1) / (a1 − a2)(a1 − a3)· · ·(a1 − an+1) + b2(x − a1)(x −a3)(x − a4)· · ·(x − an+1) / (a2 − a1)(a2 − a3)(a2 − a4)· · ·(a2 −an+1) + · · · + bn+1(x − a1)(x − a2)· · ·(x − an) / (an+1 −a1)(an+1 − a2)· · ·(an+1 − an).

Find g(a1), g(a2), · · · g(an+1).

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