Let's go through the three questions from the quiz.

Question 1: Factor $8x^2 - 50$

This is a difference of squares. It can be factored as follows:

$8x^2 - 50 = 2(4x^2 - 25) = 2(2x - 5)(2x + 5)$

Factored form: $2(2x - 5)(2x + 5)$

Question 2: Factor $4x^2 - 16x + 16$

This is a perfect square trinomial. It can be factored as follows:

$4x^2 - 16x + 16 = (2x - 4)^2$

Factored form: $(2x - 4)^2$ or $(2(x - 2))^2 = 4(x - 2)^2$

Question 3: Factor $4x^3 - 108$

Factor out the greatest common factor first, and then factor the difference of cubes:

$4x^3 - 108 = 4(x^3 - 27) = 4(x - 3)(x^2 + 3x + 9)$

Factored form: $4(x - 3)(x^2 + 3x + 9)$

Would you like further details or clarifications on these solutions?

Here are some follow-up questions to deepen understanding:

1. What are the conditions for factoring as a difference of squares?
2. How do you identify a perfect square trinomial?
3. Can a sum of cubes be factored similarly to a difference of cubes?
4. How does factoring help in solving quadratic equations?
5. What are the steps involved in factoring polynomials with common factors?

Tip: Always look for common factors before trying other factoring techniques—it simplifies the problem!