Question 1: Factorise x² + 5x + 6.

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

Question 2: Expand the factorised form (x + 4)(x + 1).

Answer: x² + 5x + 4

Question 3: Factorise x² - 9x + 20.

Answer: (x - 4)(x - 5)

Question 4: Solve for x: x² + 3x - 4 = 0 by factorising.

Answer: x = 1 or x = -4

Question 5: Factorise x² + 6x + 9.

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

Question 6: A rectangle has sides of length x + 2 and x + 3. Write an expression for its area and factorise it.

Answer: x² + 5x + 6; (x + 2)(x + 3)

Question 7: Complete the square for x² + 4x + 1 and express as (x + a)².

Answer: (x + 2)²

Question 8: Identify the mistake in factorising x² + 7x + 12 as (x + 3)(x + 4).

Answer: Correct factorisation; no mistake.

Question 9: Challenge: Factorise x² + 8x + 21 using the quadratic formula and verify the factors.

Answer: x = -3 or x = -7; factors: (x + 3)(x + 7)

Question 10: What are the roots of x² - 4x + 3? Factorise and find the solutions.

Answer: x = 1 or x = 3

Question 11: Identify the common mistake in factorising x² + 2x + 1 as (x + 1)², and correct it if necessary.

Answer: No mistake; (x + 1)² is correct for x² + 2x + 1.