Question

设多项式f(x)除以x^2-3x+2的余式为x+4而f(x)除以x^2-4x+3的余式为2x+3求

设多项式f(x)除以x^2-3x+2的余式为x+4而f(x)除以x^2-4x+3的余式为2x+3求设多项式f(x)除以x^2-3x+2的余式为x+4,而f(x)除以x^2-4x+3的余式为2x+3求
（1）函数值f(2)
（2）函数值f(3)
（3）f(x)除以x^2-5x+6的余式

Answer 1

令f(x) = A(x²-3x+2)+(x+4) = B(x²-4x+3)+(2x+3)
A(x²-3x+2) - B(x²-4x+3) = (2x+3)-(x+4)

A(x-1)(x-2) - B(x-1)(x-3) = x-1
两边同除以x-1：
A(x-2) - B(x-3) = 1

Ax-2A - Bx+3B = 1

Ax-Bx-2A+3B = 1
A=B且-2A+3B = 1
A=B=1
f(x) = (x²-3x+2)+(x+4) =(x²-4x+3)+(2x+3)

f(x) = x²-2x+6

f(2) = 2²-2*2+6 = 6
f(3) = 3²-2*3+6 = 9

f(x)÷(x²-5x+6) = (x²-2x+6)÷(x²-5x+6) = (x²-5x+6+3x)÷(x²-5x+6) = 1 + 3x/(x²-5x+6）
余3x

Answer 2

没有标点符号，看不懂。