Question 1: Factorise the expression 6x + 9.

Answer: 3(2x + 3)

Question 2: Factorise the quadratic expression x^2 + 5x + 6.

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

Question 3: Simplify the algebraic fraction: (6x^2 + 12x) / (3x).

Answer: 2x + 4

Question 4: Factorise the expression 4x^2 - 25.

Answer: (2x + 5)(2x - 5)

Question 5: Construct a quadratic expression that can be factorised as (x + 4)(x - 1).

Answer: x^2 + 3x - 4

Question 6: Identify the mistake: Factorising 3x^2 + 6x as 3(x^2 + 2).

Answer: Incorrect because x^2 + 2 is not equivalent to x^2 + 2x; the correct factorisation is 3x(x + 2).

Question 7: Factorise 2x^2 - 8x + 6 completely.

Answer: 2(x - 1)(x - 3)

Question 8: Solve for x: (x - 2)(x + 3) = 0.

Answer: x = 2 or x = -3

Question 9: Explain why the expression 9x^2 + 6x can be factorised as 3x(3x + 2).

Answer: Because both terms have a common factor of 3x, so factorising out 3x gives 3x(3x + 2).

Question 10: Challenge: Factorise 3x^3 + 6x^2 + 9x completely.

Answer: 3x(x + 1)(x + 3)

Question 11: Identify the error: Students try to factorise x^2 + 4x + 4 as (x + 2)^2 without expanding first.

Answer: No error; (x + 2)^2 correctly expands to x^2 + 4x + 4.