Factor the following trinomial. (Hint: Solve the equations first.)x²-2x-2

Answer:[tex](x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]  Step-by-step explanation:we know that The formula to solve a quadratic equation of the form [tex]ax^{2} +bx+c=0[/tex] is equal to [tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex] in this problem we have [tex]x^{2} -2x-2=0[/tex]  so [tex]a=1\\b=-2\\c=-2[/tex] substitute in the formula [tex]x=\frac{-(-2)(+/-)\sqrt{-2^{2}-4(1)(-2)}} {2(1)}[/tex] [tex]x=\frac{2(+/-)\sqrt{12}} {2}[/tex] [tex]x=\frac{2(+/-)2\sqrt{3}} {2}[/tex] [tex]x_1=\frac{2(+)2\sqrt{3}} {2}=1+\sqrt{3}[/tex] [tex]x_2=\frac{2(-)2\sqrt{3}} {2}=1-\sqrt{3}[/tex] therefore[tex]x^{2} -2x-2=(x-(1+\sqrt{3}))(x-(1-\sqrt{3}))[/tex]