To divide (12x³-7x²-7x+1) by (3x+2), we can use polynomial long division:
4x² - 3x + 1
-------------------------
3x + 2 |12x³ - 7x² - 7x + 1
12x³ + 8x²
-------------
-15x² - 7x
-15x² - 10x
------------
3x + 1
So, the quotient is 4x² - 3x + 1 and the remainder is 3x + 1. Therefore, we can write the original expression as:
(12x³-7x²-7x+1) = (3x+2)(4x²-3x+1) + (3x+1)
or
(12x³-7x²-7x+1) ÷ (3x+2) = 4x² - 3x + 1 with a remainder of 3x + 1.