Lời giải:

$(x^3-3x^2+2x-6):(x-3)=[x(x-3)+2(x-3)]:(x-3)$

$=(x-3)(x+2):(x-3)=x+2$

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$(x^3-8):(x-2)=(x-2)(x^2+2x+4):(x-2)=x^2+2x+4$

a) x = 2 7                         b) x = 2.

c) x = 2                          d) x = 1.

1) \(\left(x^3-8\right):\left(x-2\right)=\left[\left(x-2\right)\left(x^2+2x+4\right)\right]:\left(x-2\right)=x^2+2x+4\)

2) \(\left(x^3-1\right):\left(x^2+x+1\right)=\left[\left(x-1\right)\left(x^2+x+1\right)\right]:\left(x^2+x+1\right)=x-1\)

3) \(\left(x^3+3x^2+3x+1\right):\left(x^2+2x+1\right)=\left(x+1\right)^3:\left(x+1\right)^2=x+1\)

4) \(\left(25x^2-4y^2\right):\left(5x-2y\right)=\left[\left(5x-2y\right)\left(5x+2y\right)\right]:\left(5x-2y\right)=5x+2y\)

1: \(=x^2+1\)

3: \(=\left(x-y-z\right)^2\)

a, \(A=2x^3-9x^5+3x^5-3x^2+7x^2-12=-6x^5+2x^3+4x^2-12\)

b, \(B=2x^4+x^2+2x-2x^3-2x^2+x^2-2x+1=2x^4-2x^3+1\)

c, \(C=2x^2+x-x^3-2x^2+x^3-x+3=3\)

6: \(\left(2x^3-5x^2+6x-15\right):\left(2x-5\right)\)

\(=\frac{x^2\left(2x-5\right)+3\left(2x-5\right)}{2x-5}\)

\(=\frac{\left(2x-5\right)\left(x^2+3\right)}{2x-5}=x^2+3\)

2: \(\frac{2x^4-5x^2+x^3-3-3x}{x^2-3}\)

\(=\frac{2x^4-6x^2+x^3-3x+x^2-3}{x^2-3}\)

\(=\frac{2x^2\left(x^2-3\right)+x\cdot\left(x^2-3\right)+\left(x^2-3\right)}{x^2-3}=2x^2+x+1\)

5: \(\left(2x^3+5x^2-2x+3\right):\left(2x^2-x+1\right)\)

\(=\frac{2x^3-x^2+x+6x^2-3x+3}{2x^2-x+1}=\frac{\left(2x^2-x+1\right)\left(x+3\right)}{2x^2-x+1}\)

=x+3

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

1: \(\left(x^3-3x^2+x-3\right):\left(x-3\right)\)

\(=\frac{x^2\left(x-3\right)+\left(x-3\right)}{x-3}=x^2+1\)

ảnh lỗi r ạ

Lỗi rùi

`P(x)=\(4x^2+x^3-2x+3-x-x^3+3x-2x^2\)

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

`= 2x^2+3`

`Q(x)=`\(3x^2-3x+2-x^3+2x-x^2\)

`= -x^3+(3x^2-x^2)+(-3x+2x)+2`

`= -x^3+2x^2-x+2`

`P(x)-Q(x)-R(x)=0`

`-> P(X)-Q(x)=R(x)`

`-> R(x)=P(x)-Q(x)`

`-> R(x)=(2x^2+3)-(-x^3+2x^2-x+2)`

`-> R(x)=2x^2+3+x^3-2x^2+x-2`

`= x^3+(2x^2-2x^2)+x+(3-2)`

`= x^3+x+1`

`@`\(\text{dn inactive.}\)

a: P(x)-Q(x)-R(x)=0

=>R(x)=P(x)-Q(x)

=2x^2+3+x^3-2x^2+x-2

=x^3+x+1