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

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

Question 2: Factorise the quadratic x² - 3x - 10.

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

Question 3: Factorise the quadratic x² + 4x + 4.

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

Question 4: Factorise the quadratic x² - x - 12.

Answer: (x - 4)(x + 3)

Question 5: Factorise the quadratic x² + 2x - 15.

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

Question 6: Solve for x: x² + 7x + 10 = 0 by factorising.

Answer: x = -2 or x = -5

Question 7: Factorise completely: x² + 6x + 9 and verify the factors.

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

Question 8: A rectangle's length is modeled by x + 2 and width by x - 1. Write an expression for its area when x=3, then factorise it.

Answer: The area = (x + 2)(x - 1); at x=3, area = 5×2=10.

Question 9: Construct a quadratic expression with roots at x=2 and x=-4, then expand and factorise it.

Answer: x² + 2x - 8

Question 10: Identify the mistake in factorising x² + 4x + 5 as (x + 2)(x + 2). Explain and correct it.

Answer: Incorrect because x² + 4x + 5 cannot be factored into real factors; the correct factors involve complex numbers.

Question 11: Challenge: Find all possible factor pairs of x² + 13x + 40 and verify which pair correctly factorises the quadratic.

Answer: Pairs: (x + 5)(x + 8), (x + 4)(x + 10); correct pair: (x + 5)(x + 8).