Given roots are (-3) and ([tex]2 + \sqrt{3} [/tex])
[tex]2 + \sqrt{3} [/tex] is one of the root. So other root is [tex]2 - \sqrt{3}[/tex]
So we have three roots -3 , [tex]2 + \sqrt{3} [/tex] and [tex]2 - \sqrt{3} [/tex]
Now we write the all the roots in factor form
[tex](x -(-3)) (x- (2 + \sqrt{3}) (x- (2 - \sqrt{3})[/tex]
[tex](x + 3) (x- 2 - \sqrt{3}) (x- 2 + \sqrt{3})[/tex]
Now we multiply last two parenthesis
[tex](x + 3) (x^2- 2x +x\sqrt{3} -2x + 4 -2\sqrt{3} - x \sqrt{3} +2 \sqrt{3} - 3)[/tex]
Now combine like terms
[tex](x + 3) (x^2- 4x+1)[/tex]
[tex](x^3 -4x^2 +x + 3x^2-12x +3)[/tex]
[tex](x^3 - x^2 - 11x +3)[/tex]
