[tex]y=3x^2-5x-2\\\\a=3,\ b=-5,\ c=-2\\\\\Delta=b^2-4ac=(-5)^2-4\cdot3\cdot(-2)=25+24=49\\\\\sqrt{\Delta}=7\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{5-7}{6}=-\dfrac{1}{3}\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{5+7}{6}=2\\\\y=a(x-x_1)(x-x_2)\\\\\boxed{y=3\Big(x+\dfrac{1}{3}\Big)(x-2)}[/tex]
[tex]y=2x^2-x+3\\\\a=2,\ b=-1,\ c=3\\\\\Delta=b^2-4ac=(-1)^2-4\cdot2\cdot3=1-24=-23<0[/tex]
Postać iloczynowa nie istnieje.
[tex]y=-x^2-2x-1\\\\y=-(x^2+2x+1)\\\\\boxed{y=-(x+1)^2}[/tex]