$\text{a)}{x}^3-9x^2+2x-18=0$

$x^2\left(x-9\right)+2\left(x-9\right)=0$

$\left(x-9\right)\left(x^2+2\right)=0$

$x-9=0\text{lub}\underset{\text{roˊwnanie sprzeczne}}{x^2+2=0}$

$x=9$

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$\text{b)}2x^3+x^2-8x-4=0$

$x^2\left(2x+1\right)-4\left(2x+1\right)=0$

$\left(2x+1\right)\left(x^2-4\right)=0$

$2x+1=0\text{lub}{x}^2-4=0$

$2x=-1\mid :2\text{lub}{x}^2=4$  

$x=-\frac{1}{2}\text{lub}x=2\text{lub}x=-2$

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$\text{c)}{x}^5+5x^4+x^3+5x^2=0$

$x^2\left(x^3+5x^2+x+5\right)=0$  

$x^2\left[x^2\left(x+5\right)+\left(x+5\right)\right]=0$  

$x^2\left(x+5\right)\left(x^2+1\right)=0$  

$x^2=0\text{lub}x+5=0\text{lub}\underset{\text{roˊwnanie sprzeczne}}{x^2+1=0}$  

$x=0\text{lub}x=-5$  

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$\text{d)}3x^4-5x^3-6x^2+10x=0$

$x\left(3x^3-5x^2-6x+10\right)=0$  

$x\left[x^2\left(3x-5\right)-2\left(3x-5\right)\right]=0$  

$x\left(3x-5\right)\left(x^2-2\right)=0$  

$x=0\text{lub}3x-5=0\text{lub}{x}^2-2=0$  

$x=0\text{lub}3x=5\mid :3\text{lub}{x}^2=2$  

$x=0\text{lub}x=\frac{5}{3}\text{lub}x=-\sqrt{2}\text{lub}x=\sqrt{2}$  

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$\text{e)}{x}^5-4x^3-8x^2+32=0$

$x^3\left(x^2-4\right)-8\left(x^2-4\right)=0$

$\left(x^2-4\right)\left(x^3-8\right)=0$

$x^2-4=0\text{lub}{x}^3-8=0$

$x^2=4\text{lub}{x}^3=8$  

$x=-2\text{lub}x=2\text{lub}x=2$

$x=-2\text{lub}x=2$  

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$\text{f)}{x}^3-3\sqrt{2}{x}^2+\sqrt{2}x-6=0$

$x^2\left(x-3\sqrt{2}\right)+\sqrt{2}x-3\sqrt{2}\cdot \sqrt{2}=0$  

$x^2\left(x-3\sqrt{2}\right)+\sqrt{2}\left(x-3\sqrt{2}\right)=0$  

$\left(x-3\sqrt{2}\right)\left(x^2+\sqrt{2}\right)=0$  

$x-3\sqrt{2}=0\text{lub}\underset{\text{roˊwnanie sprzeczne}}{x^2+\sqrt{2}=0}$  

$x=3\sqrt{2}$