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数学之美团为你解答
4x^4+2x^3+x-3 = a(x-2)^4+b(x-2)^3+c(x-2)^2+d(x-2)+e
令 x = 2 得 e = 79
令 x=1得 a - b + c - d + 79 = 4
令 x = 3得 a+b+c+d+79 = 378
两式相加 2a+2c+79*2 = 382
a+c = 112 ①
两式相减 2b+2d = 374 ,b+d = 187 ②
令 x=0得 16a - 8b +4c - 2d + 79 = - 3
令 x = 4得 16a+8b+4c+2d+79 = 1153
两式相加 32a + 8c +79*2 = 1150
4a+c = 124 ③
两式相减 16b+4d = 1156
4b + d = 289 ④
由①③解得 a = 4,c = 108
由②④解得 b = 34,d = 153
∴ 4x⁴+2x³+x - 3 = 4(x-2)⁴ + 34(x-2)³+108(x-2)²+153(x-2)+79