$$ \definecolor{crimBlue}{rgb}{0.196,0.467,0.533} \definecolor{crimOrange}{rgb}{0.969,0.553,0.149} \definecolor{crimGreen}{rgb}{0.498,0.694,0.302} $$
Complete the steps to factor $&12x^3 - 9x^2 + 8x - 6$& by grouping.

Step 1: Group the first two terms and the second two terms.

Step 2: What is the greatest common factor of group 1?
$&3x$&
$&6x$&
$&3x^2$&

Step 3: What is the greatest common factor of group 2?
$&2$&
$&2x$&
$&3x$&

Step 4: What is the common factor in both terms of the resulting expression?
$&3x^2$&
$&4x$&
$&4x-3$&

Step 5: Use the distributive property to write the factored form of the polynomial.
$&3x^2(4x-3)$&
$&(4x-3)(3x^2+2)$&

$&12x^3 - 9x^2 + 8x - 6 $&
$&= (12x^3 - 9x^2)$&
    group 1
  +  $&(8x - 6)$&
      group 2


$$= 3x^2(4x-3) + (8x - 6)$$
$$= 3x^2(4x - 3) + 2(4x - 3)$$
$$= 3x^2\enclose{circle}[mathcolor="red"]{(4x - 3)} + 2\enclose{circle}[mathcolor="red"]{(4x - 3)}$$
$$ = (4x - 3)(3x^2 + 2)$$