To factor the expression completely, we first need to simplify it. Let’s start by rewriting it clearly:
3x² – 3x + 4 – 3x + 1x – 4 – 3x + 4x – 1 + 3x² + 2 – 3x + 4x – 1
Now, combine like terms:
- 3x² + 3x² = 6x²
- -3x – 3x + 1x – 3x + 4x – 3x = -4x
- 4 – 4 – 1 + 2 – 1 = 0
This simplifies our expression to:
6x² – 4x
Next, we can factor out the greatest common factor (GCF), which is 2x:
2x(3x – 2)
Thus, the completely factored form of the expression is:
2x(3x – 2)
This shows that we have successfully factored the original expression.