Question 1: Factor the expression: x^2 - 16.

Answer: (x - 4)(x + 4)

Question 2: Identify the pattern in the sequence: 9, 16, 25, 36, ... What is the next term?

Answer: 49

Question 3: Expand and factor: a^2 - 81.

Answer: (a - 9)(a + 9)

Question 4: Plot the graph of y = x^2 - 25 for x from -5 to 5.

Answer: Student draws parabola crossing points at y=0 when x= ±5.

Question 5: Explain why x^2 - 49 can be written as (x - 7)(x + 7).

Answer: Because x^2 - 49 is a difference of squares, which factors as (x - 7)(x + 7).

Question 6: Find the value of x if x^2 - 36 = 0.

Answer: x=±6

Question 7: Identify the pattern in the expressions: 25 - 4, 36 - 9, 49 - 16, ... What is the next expression?

Answer: 64 - 25

Question 8: Construct a binomial that is the difference of two squares for the number 100.

Answer: (x - 10)(x + 10)

Question 9: Identify the error: Simplify x^2 - 49 as x^2 - 7^2 and factor it as (x - 7).

Answer: Incorrect; it should be factored as (x - 7)(x + 7).

Question 10: Given the expression x^2 - 64, show two different ways to factor it.

Answer: (x - 8)(x + 8) or x^2 - 64 = (x - 8)(x + 8)

Question 11: Challenge: If a^2 - b^2 = (a - b)(a + b), find the factors when a= x+3 and b= x-1.

Answer: (x+3 - (x-1))(x+3 + (x-1)) = (4)(2x+2) = 8(x+1)