Question

待定系数法题目将 5x^3—6x^2+10 表示成 a(x-1)^3+b(x-1)^2+c(x-1)+d 的形式求求大家

Answer 1

a(x-1)^3+b(x-1)^2+c(x-1)+d

=ax^3-3ax^2+3ax-a+bx^2-2bx+b+cx-c+d

=ax^3-(3a-b)x^2+(3a-2b+c)x+(-a+b-c+d)

a=5

3a-b=6 => b=9

3a-2b+c=0 =>c=3

-a+b-c+d=10 => b=9