The expression x2y - 2xy - 24y can be factored by first factoring out a common factor of y.
after the common factor is removed, the remaining factor is a

quadratic

Step-by-step explanation:

Given

x²y - 2xy - 24y ← factor out y from each term

= y(x² - 2x - 24) ← quadratic factor

To factor the quadratic

Consider the factors of the constant term ( - 24) which sum to give the coefficient of the x- term (- 2)

The factors are - 6 and + 4, since

- 6 × 4 = - 24 and - 6 + 4 = - 2, hence

x² - 2x - 24 = (x - 6)(x + 4) and

x²y  - 2xy - 24y = y(x - 6)(x + 4) ← in factored form

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)