Question

已知x³-16x²+mx-n除以x²-2x+3所得余式为-18x+15,求m,n的值.

Answer 1

x^3-16x^2+mx-n x^2-2x+3

=x(x^2-16x+m)-n

=x(x^2-2x-14x+3-3+m)-n

=x(x^2-2x+3-14x+m-3)-n

=x(x^2-2x+3)-14x^2+mx-3x-n

=x(x^2-2x+3)-14x^2+28x+mx-31x-42+42-n

=x(x^2-2x+3)-14(x^2-2x+3)+(m-31)x+42-n

m-31=-18 m=13

42-n=15 n=27