Answer:
[tex](x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]
Step-by-step explanation:
Start with the discriminant of the trinomial
[tex]x^2-6x+4[/tex]
The discriminant is
[tex]D=b^2-4ac=(-6)^2-4\cdot 1\cdot 4=36-16=20[/tex]
Now, find the roots of the trinomial using the quadratic formula
[tex]x_{1,2}=\dfrac{-b\pm \sqrt{D}}{2a}=\dfrac{-(-6)\pm \sqrt{20}}{2\cdot 1}=\dfrac{6\pm2\sqrt{5}}{2}=3\pm \sqrt{5}[/tex]
So, the factored form of the trinomial is
[tex](x-(3+\sqrt{5}))(x-(3-\sqrt{5}))=(x-3-\sqrt{5})(x-3+\sqrt{5})[/tex]
