[tex]1a)\\\\(x-2)^2-x^2=x^2-4x+4-x^2=-4x+4=4(1-x)\\\\b)\\\\x^5-4x^3=x^3(x^2-1)=x^3(x+1)(x-1)\\\\[/tex]
[tex]c)\\\\-x^2+2x+3=-(x-3)(x+1)=(3-x)(x+1)\\\\a=-1,\ \ b=2,\ \ c=3\\\\\Delta =b^2-4ac=2^2-4*(-1)*3=4+12=16\\\\\sqrt{\Delta }=\sqrt{16}=4\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-2-4}{2*(-1)}=\frac{-6}{-2}=3\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-2+4}{2*(-1)}=\frac{2}{-2}=-1[/tex]
[tex]2a)\\\\2x^4+3x^3-2x^2=0\\\\ (2x^2+3x -2)x^2=0\\\\2x^2+3x-2=0\ \ lub\ \ x=0\\\\a=2,\ \ b=3,\ \ c=-2\\\\\Delta =b^2-4ac=3^2-4*2*(-2) = 9+16=25\\\\\sqrt{\Delta }=\sqrt{25}=5\\\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{ -3-5}{2*2}=\frac{-8}{4}=-2\\\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{ -3+5}{2*2}=\frac{2}{4}= \frac{1}{2}\\\\x\in\left\{-2;0;\frac{1}{2} \right\}[/tex]
[tex]b)\\\\3x^3-x^2-12x+4=0\\\\ x^2(3x-1)-4(3x-1)=0\\\\(x^2-4)(3x-1)=0\\\\(x-2)(x+2)(3x-1)=0\\\\x-2=0\ \ lub\ \ x+2=0\ \ lub\ \ 3x-1=0\\\\x=2\ \ lub\ \ x=-2\ \ lub\ \ x=\frac{1}{3}\\\\x\in\left\{ -2;\frac{1}{3};2\right\}[/tex]
[tex]c)\\\\ (x^2-4)(x^2-3)=0\\\\(x-2)(x+2)(x-\sqrt{3})(x+\sqrt{3})=0\\\\x-2=0\ \ lub\ \ x+2=0\ \ lub\ \ x-\sqrt{3}=0\ \ lub\ \ x+\sqrt{3}=0\\\\x=2 \ \ lub\ \ x=-2 \ \ lub\ \ x=\sqrt{3} \ \ lub\ \ x=-\sqrt{3}\\\\x\in\left\{-2;2;-\sqrt{3};\sqrt{3} \right\}[/tex]
