F.4續多項式除法

1:
px^3+qx^2-2x+3=(2x^2+3x+r)(x-1)+4
R.H.S.=2x^3+3x^2-2x^2+rx-3x-r+4
=2x^3+x^2+(r-3)x+(4-r)
By comparing coefficients of like terms:
p=2
q=1
r-3=-2
r=1

For g(x)=4
i.e. (2x^2+3x+r)(x-1)+4=4
(x-1)(2x^2+3x+1)=0
(x-1)(2x+1)(x+1)=0
x=1 , -1/2 or -1
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2:
2x^3+px^2+qx+8=(2x-1)(x^2+4x-3)+5
R.H.S.=2x^3+8x^2-x^2-6x-4x+3+5
=2x^3+7x^2-10x+8
By comparing coefficients of like terms:
p=7
q=-10

被除式 = 商式 × 除式 + 餘式
1a) px^3+qx^2-2x+3 = (2x^2+3x+r)(x-1) + 4
2) 2x^3+px^2+qx+8= (x^2+4x-3)(2x-1) + 5