Question

What is 12x3 – 9x2 – 4x + 3 in factored form?

Answer 1

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