Do you always use the property of distribution when multiplying monomials and polynomials? Explain why or why not. In what situations would distribution become important?

Imagine your younger relative—of middle school age—was taking an algebra course and asked for your help. How would you teach the multiplication of polynomials to her?

What is the greatest common factor of an algebraic expression? How do you know when you have found the greatest one? Give an example and explain how you know you have found the greatest common factor.

Explain how to factor the following trinomials forms: x2 + bx + c and ax2 + bx + c. Is there more than one way to factor this? Show your answer using both words and mathematical notation.

How do you factor the difference of two squares? How do you factor the perfect square trinomial? How do you factor the sum and difference of two cubes? Which of these three makes the most sense to you? Explain why.

What one area from the readings in Week Two are you most comfortable with? Why do you think that is? Using what you know about this area, create a discussion question that would trigger a discussion—that is, so there is no single correct answer to the question.

Explain the five steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make rational equations easier to complete or understand?

What are the two steps for simplifying radicals? Can either step be deleted? If you could add a step that might make simplifying radicals easier or easier to understand, what step would you add?

Explain the four steps for solving quadratic equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make solving quadratic equations easier or easier to understand?

Is the compound interest formula—such as would be used to calculate a car loan—an example of a function? If yes, of what type of function is it an example? Why might you identify it with that type of function?

From the concepts you have learned in this course, provide a real-world application of something that you think has been the most valuable to you? Why has it been valuable?

How do you think you will use the information you learned in this course in the future? Which concepts will be most important to you? Explain why. Which do you anticipate will be the least important? Explain why.

Can you think of one real-world example of when the concept of functions might be useful? Do you think you will ever use functions in your life to solve problems? If yes, explain how and why; if no, explain why not.

What one concept learned in this course was the easiest for you to grasp? Why do you think it was easy for you? Which was the hardest? What would have made that hard-to-learn concept easier to learn?