Complete the steps to factor 12x3 − 9x2 + 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
3x2

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?
3x2
4x
4x − 3

Step 5: Use the distributive property to write the factored form of the polynomial.
3x2(4x − 3)
(4x − 3)(3x2 + 2)

12x3 − 9x2 + 8x − 6
= (12x3 − 9x2)
    Group 1
  +  (8x − 6)
      Group 2


= 3x2(4x − 3) + (8x − 6)
= 3x2(4x − 3) + 2(4x − 3)
Common factor: 4x − 3
= (4x − 3)(3x2 + 2)