`(-x^4+2x-3x^2):(x-2)`

`=[-x(x^3+3x-2)]:(x-2)`

`=[-x(x^3-2x^2+2x^2-4x+7x-14+12)]:(x-2)`

`={-x[x^2(x-2)+2x(x-2)+7(x-2)]-12x+24-24}:(x-2)`

`=[-x(x-2)(x^2+2x+7)-12(x-2)-24]:(x-2)`

`=-x(x^2+2x+7)-12` và dư `-24`

`=-x^3-2x^2-7x-12` và dư `-24`

\(\dfrac{-x^4-3x^2+2x}{x-2}\)

\(=\dfrac{-x^4+2x^3-2x^3+4x^2-7x^2+14x-12x+24-24}{x-2}\)

\(=-x^3-2x^2-7x-12-\dfrac{24}{x-2}\)

\(\dfrac{-x^4-3x^2+2x}{x-2}\)

\(=\dfrac{-x^4+2x^3-2x^3+4x^2-7x^2+14x-12x+24-24}{x-2}\)

\(=-x^3-2x^2-7x-12+\dfrac{-24}{x-2}\)

b: \(\dfrac{A\left(x\right)}{B\left(x\right)}=\dfrac{x^4-\dfrac{1}{2}x^3+\dfrac{1}{2}x^3-\dfrac{1}{4}x^2+\dfrac{9}{4}x^2-\dfrac{9}{8}x-\dfrac{15}{8}x+\dfrac{15}{16}+a-\dfrac{1}{16}}{2x-1}\)

Để A(x) chia hết cho B(x) thì a-1/16=0

hay a=1/16

a: \(=\dfrac{x\left(x^2+x-2\right)}{x+2}=\dfrac{x\left(x+2\right)\left(x-1\right)}{x+2}=x^2-x\)

b: \(=\dfrac{x^3-3x^2+2x+24}{x+2}=\dfrac{x^3+2x^2-5x^2-10x+12x+24}{x+2}=x^2-5x+12\)

`-1/3x^5y^2:(-2xy)-(x^2+2x+1):(x+1)`

`=-1/3:(-2).(x^5:x).(y^2:y)-(x+1)^2:(x+1)`

`=-1/6x^4y-(x+1)`

`=-1/6x^4y-x-1`

\(\dfrac{-1}{3}x^5y^2:\left(-2xy\right)-\left(x^2+2x+1\right):\left(x+1\right)\)

\(=\dfrac{1}{6}x^4y-x-1\)

\(x^2\left(y-1\right)-4\left(y-1\right)\\ =\left(y-1\right)\left(x^2-4\right)=\left(y-1\right)\left(x-2\right)\left(x+2\right)\)

\(=\left(y-1\right)\left(x-2\right)\left(x+2\right)\)

\(x^2\left(y-1\right)-4\left(y-1\right)\\ =\left(x^2-4\right)\left(y-1\right)\\ =\left(x-2\right)\left(x+2\right)\left(y-1\right)\)

a: \(=\dfrac{2xy\left(2x^2y-4x+5\right)}{2xy}=2x^2y-4x+5\)

b: \(=\dfrac{x^2y\left(7x^2y-2y-5x^2y^3\right)}{3x^2y}=\dfrac{7}{3}x^2y-\dfrac{2}{3}y-\dfrac{5}{3}x^2y^3\)