Question 1: Factorise the quadratic expression x² + 5x + 6.

Answer: (x + 2)(x + 3)

Question 2: Find the value of c if the quadratic x² + 7x + c factors into (x + 1)(x + 6).

Answer: c = 6

Question 3: Construct a quadratic pattern with roots at x = -2 and x = 3. Write the expression in simplified form.

Answer: x² - x - 6

Question 4: Plot the graph of y= -x² + 4x + 5 on the grid.

Answer: Student plots parabola opening downward with vertex at (2, 9).

Question 5: A pattern uses tiles arranged in a quadrilateral with dimensions based on (x + 3)(x + 4). How many tiles are needed when x=2?

Answer: 35

Question 6: If a rectangle's area is described by x² + 9x + 14, find its length and width.

Answer: Factors as (x + 2)(x + 7), so dimensions are x + 2 and x + 7.

Question 7: Identify the mistake: The quadratic x² + 4x + 3 was incorrectly factored as (x + 4)(x + 3).

Answer: Incorrect; it should be (x + 1)(x + 3).

Question 8: Expand and simplify: (x + 5)(x + 2).

Answer: x² + 7x + 10

Question 9: In an art pattern, the number of tiles in a row is modeled by x + 3, and the number of columns by x + 2. Write an expression for the total number of tiles and evaluate when x=4.

Answer: (x + 3)(x + 2); when x=4, total tiles = (7)(6) = 42.

Question 10: Factorise the quadratic: x² + 8x + 15.

Answer: (x + 3)(x + 5)

Question 11: Challenge: A pattern uses a quadratic expression x² + bx + c, where roots are at x= -1 and x= -4. Find the quadratic expression.

Answer: x² + 5x + 4