Question 1: Factorise the quadratic expression 6x² + 11x + 3.

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

Question 2: Expand and simplify the factorised form (4x + 5)(x + 2).

Answer: 4x² + 13x + 10

Question 3: Factorise the quadratic: 8x² + 10x + 3.

Answer: (4x + 1)(2x + 3)

Question 4: What is the common factor in the quadratic 14x² + 21x?

Answer: 7x

Question 5: Factorise 9x² + 24x + 16.

Answer: (3x + 4)^2

Question 6: Solve for x: 3x² - 5x - 2 = 0 using factorisation.

Answer: x = 2/3 or x = -1

Question 7: Construct a quadratic expression of the form ax² + bx + c, where a=2, b= -7, c= 3. Write its expanded form.

Answer: 2x² - 7x + 3

Question 8: Identify the error in factorising 4x² + 5x + 1 as (2x + 1)(2x + 1).

Answer: The correct factorisation is (4x + 1)(x + 1); the given is wrong because it does not expand correctly.

Question 9: Factorise 10x² + 7x - 3.

Answer: (5x - 3)(2x + 1)

Question 10: A rectangular garden has dimensions represented by algebraic expressions ax + b and cx + d. If the area is quadratic (ax + b)(cx + d), explain how factorising helps in finding dimensions when area is given.

Answer: Factorising the quadratic expression of the area helps find possible values of x that satisfy the area, thus determining the dimensions.

Question 11: Simplify and factorise 12x² + 18x.

Answer: 6x(2x + 3)

Question 12: Challenge: Factorise 18x² + 33x + 15 completely.

Answer: 3(6x + 5)(x + 1)