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)(√(3)x+1)(√(3)x-1)`
So
`12x^(3)-9x^(2)-4x+3` in factored form is
`(4x-3)(√(3)x+1)(√(3)x-1)`.