In an experiment, a scientist obtained the following data.    x  0  1        -1              y -5 -3 -15 Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial : P2(x) = −5 + 2x − 4x(x−1) Now, the scientist wants to do more experiment and got two more points (2, 39) and (−2,−9). Therefore, the total data is the following. x 0 1 -1 2 -2 y -5 -3 -15 39 -9 Again by apply Newton's interpolating polynomial method, the scientist obtained the following polynomial P5(x) = a + 2x + bx(x−1) + cx(x−1)(x+1) + 3x(x−1)(x+1)(x+d). Then, a= b= c= d=

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A: This is a problem of Number Theory.