Question

数已知关于x的多项式ax^3+bx^2+cx+d除以x-1

Answer 1

设f(x)=ax^3+bx^+cx+d,

由余数定理,f(1)=a+b+c+d=1,①

f(2)=8a+4b+2c+d=3,②

②-①,7a+3b+c=2,

c=2-7a-3b,

代入①,2-6a-2b+d=1,

d=6a+2b-1,

f(x)=ax^3+bx^+(2-7a-3b)x+6a+2b-1

=(x^2-3x+2)(ax+3a+b)+2x-1,

∴ax^3+bx^+cx+d除以（x-1)(x-2)时,所得的余式是2x-1