Factorize completely: 3x²-2xy-y
Does not factor in any useful way.
To factorize the expression 3x² - 2xy - y completely, we need to find the common factors of the terms and then factor out those common factors. Let's break it down step by step:
Step 1: Group the terms based on common factors:
3x² - 2xy - y = (3x²) - (2xy) - y
Step 2: Factor out the greatest common factor (GCF) from each group:
In the first group, the GCF is 3x². Divide each term by 3x²:
(3x²) - (2xy) - y = 3x² - 2xy/3x² - y/3x²
Step 3: Simplify if possible:
In this case, we cannot simplify any further, so let's move on to the next step.
Step 4: Factor out the GCF from the entire expression:
Now that we have factored out the GCF from each group, let's factor it out from the entire expression:
3x² - 2xy/3x² - y/3x² = (3x² - 2xy - y)/(3x²)
Step 5: Simplify the expression further if possible:
In this particular case, we cannot factor out any common factors or simplify the expression any further. Therefore, the completely factored form of the expression 3x² - 2xy - y is (3x² - 2xy - y)/(3x²).
Note: Sometimes, expressions cannot be factored completely, and they might remain in this factored form.