Final answer:
The factor of the quadratic expression 4x² - 8xy - 60y is (x + 3y), which corresponds to option A.
Step-by-step explanation:
To determine which of the given options represents a factor of the quadratic expression 4x² - 8xy - 60y, we need to factor the expression completely. We start by looking for a common factor that each term in the expression shares. In this case, we can see that 4 is a common factor, so we can factor it out:
4x² - 8xy - 60y = 4(x² - 2xy - 15y)
Now, we need to factor the quadratic x² - 2xy - 15y inside the parentheses. To do this, we look for two numbers that multiply to give -15 (the constant term) and add to give -2 (the coefficient of the middle term). The numbers -5 and 3 satisfy these conditions, so we can write:
x² - 2xy - 15y = (x - 5y)(x + 3y)
So, the completely factored form of 4x² - 8xy - 60y is:
4(x² - 2xy - 15y) = 4(x - 5y)(x + 3y)
Looking at the options given, we can see that option A, which is (x + 3y), is indeed a factor of the quadratic expression.