There are 300 students in the 9th grade and each student is assigned a locker. The 300 students start down the hall one at a tim
e. The first student opens every locker. The second student closes all the lockers that are multiples of 2. The third student changes the lockers that are multiples of 3 (which means if a locker is closed, they open it. If the locker is open, they close it.) The fourth student changes all the lockers that are multiples of 4. This continues until the 300th student changes the 300th locker. Then, the principal walks down the hall, and changes all the lockers that are prime numbers. At the end, how many lockers will be closed?
We can factor x^2 -16 = 0 by recognizing that it is a difference of squares. That means we can factor the equation to (x-4)(x+4) = 0. By using the Zero Product Property we know that either (x-4) or (x+4) is equal to 0. That means that x either equals -4 or 4.
