Question 1: Factorise the quadratic expression: 6x² + 11x - 35.

Answer: (3x - 5)(2x + 7)

Question 2: Express the quadratic 8x² - 14x - 48 as a product of its factors.

Answer: (4x + 6)(2x - 4)

Question 3: Factorise 9x² + 24x + 16 and verify your answer.

Answer: (3x + 4)²

Question 4: Solve for x: 4x² - 7x - 2 = 0 by factorisation.

Answer: x = 2/4 or x= -1/2 (from factors (2x + 1)(2x - 2) = 0)

Question 5: Construct a quadratic expression with roots at x= -3 and x= 4, in the form ax² + bx + c, where a=2.

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

Question 6: Determine the missing coefficient c in the quadratic 5x² + 3x + c, if it factors into (x + 1)(5x + c).

Answer: c = 5

Question 7: Identify the error in the following factorisation: 4x² + 12x + 9 = (2x + 3)² (correct), but students mistakenly write (2x + 3)(2x + 3) as (2x + 4)(x + 2).

Answer: Incorrect expansion; the correct factors are (2x + 3)(2x + 3).

Question 8: Factorise the quadratic: 12x² + 7x - 10.

Answer: (4x - 5)(3x + 2)

Question 9: Given the quadratic expression 10x² + 25x + c, find the value of c such that it factors into (5x + 5)(2x + ?).

Answer: 1

Question 10: Challenge: For what values of c does the quadratic 3x² + 6x + c factorise into the product of two binomials with integer coefficients?

Answer: c must be a perfect square or match the discriminant condition for factorisation, e.g., c=1, 0, 4, 9, etc.

Question 11: Identify and correct the mistake: factorising 2x² + 8x + 6 was incorrectly done as (2x + 2)(x + 3) instead of the correct factors.

Answer: Incorrect factors; the correct factorisation is 2(x + 1)(x + 3).