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Polynomials, Cubic Equations and Partial Fractions - Determining Model Coefficients Using Linear Systems

Polynomials, Cubic Equations and Partial Fractions - Determining Model Coefficients Using Linear Systems

Find the polynomial \( P(x) \) of least degree satisfying \( P(1) = 2, P(2) = 3, P(3) = 5, P(4) = 8\).
Then find \( P(5)\).

Solution:

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Answer:\(P(x)=\dfrac{x^2-x+4}{2}\), \(P(5)=12\).

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