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polynomial interpolation

Source: LIMIT 2019 CAS2 P1

April 28, 2021
algebrapolynomial

Problem Statement

Let p(x)p(x) be a polynomial of degree 44 with leading coefficient 11. Suppose p(1)=1p(1)=1, p(2)=2p(2)=2, p(3)=3p(3)=3 and p(4)=4p(4)=4. Then p(5)=p(5)=? <spanclass=′latex−bold′>(A)</span> 5<span class='latex-bold'>(A)</span>~5 <spanclass=′latex−bold′>(B)</span> 256<span class='latex-bold'>(B)</span>~\frac{25}6 <spanclass=′latex−bold′>(C)</span> 29<span class='latex-bold'>(C)</span>~29 <spanclass=′latex−bold′>(D)</span> 35<span class='latex-bold'>(D)</span>~35
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