Question

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請問綠色是怎麼變成黃色那樣的

題設f(x)為一多項式,已知xf(x)除以x+x+1,所得的餘式為-2x-1,而f(x)除以
x+x+1 所得的餘式為x+1,則k=

f(x)除以x+x+1之餘式為x+1
(x²+kx+1)q(x)+(x+1)
:: f(x) =
<>xf(x)=xx (x²+x+1)q(x) + (x²+x)
=xx (x²+x+1)q(x) +1×(x²+kx+1)
+((1-k)x-1)
= (x²+kx+1) [xq (x) +1]+[(1-k)x-1)

2
1
x²+x+1) x² +
X
x² + k x+1 E-
(1−k)x—1____x=
又xf(x)除以x+x+1之餘式為-2x-1
令1-k=-2k=3(mip