Final answer:
To find a factor of the expression 4x²y - 24x² - 24y - 144, we can factor out common terms and simplify the expression to (y - 6). Option 1 is the correct answer.
Step-by-step explanation:
To find a factor of the expression 4x²y - 24x² - 24y - 144, we can factor out common terms from each term of the expression.
Starting with the first two terms, 4x²y - 24x², we can factor out a common factor of 4x²:
4x²y - 24x² = 4x²(y - 6).
Next, we can factor out a common factor of -24 from the last two terms, -24y - 144:
-24y - 144 = -24(y + 6).
Combining the factored terms, we have:
4x²(y - 6) - 24(y + 6).
This expression can be simplified further:
4x²(y - 6) - 24(y + 6) = 4x²y - 24x² - 24y - 144.
From this simplification, we can see that the factor of the expression is (y - 6). Therefore, the correct answer is option 1) 3.