(30 pts.) Given the four data points (-1,1), (0,1), (1,2),(2,0), determine the interpolating cubic polynomial using...

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(30 pts.) Given the four data points (-1,1), (0,1), (1,2),(2,0), determine the interpolating cubic polynomial using the monomial basis; using the Lagrange basis; • using the Newton basis. Show that the three representations give the same polynomial. (30 pts.) Given the four data points (-1,1), (0,1), (1,2),(2,0), determine the interpolating cubic polynomial using the monomial basis; using the Lagrange basis; • using the Newton basis. Show that the three representations give the same polynomial.