Question

设f(x)=x^3-3px+2q ,g(x)=x^2-2x+1,试求g(x)能整除f(x)的条件

设g(f)=x^3-3x^2-x-1,g(x)=3x^2-2x+1,求用g(x)去除g(f)所得商和因式

Answer 1

x³-3x²-x-1=(3x²-2x+1)(x/3+a)+(bx+c)x³-3x²-x-1=x³+(3a-2/3)x²+(1/3-2a+b)x+a+c所以-3=3a-2/3-1=1/3-2a+b-1=a+ca=-7/9b=-26/9c=-2/9所以商式=x/3-7/9余式=-26x/9-2/9