Let's try grouping terms by common factors:
[tex]12x^{3}-9x^{2}-4x+3=(12x^{3}-4x)+(-9x^{2}+3)[/tex]
Then, take out the factors:
[tex](12x^{3}-4x)+(-9x^{2}+3)=4x(3x^{2}-1)-3(3x^{2}-1)[/tex]
We can reduce further:
[tex]4x(3x^{2}-1)-3(3x^{2}-1)=(4x-3)(3x^{2}-1)=(4x-3)(\sqrt{3}x+1)(\sqrt{3}x-1)[/tex]
So [tex]12x^{3}-9x^{2}-4x+3[/tex] in factored form is [tex](4x-3)(\sqrt{3}x+1)(\sqrt{3}x-1)[/tex].
