Question 1: Factorise and solve x² + 5x + 6 = 0.

Answer: x = -2 or x = -3

Question 2: Factorise and solve x² - 3x - 10 = 0.

Answer: x = 5 or x = -2

Question 3: Factorise and solve x² + 4x + 4 = 0.

Answer: x = -2

Question 1: A rectangular garden's length is modeled by x + 3 meters, and its width by x meters. The area is given by the quadratic x² + 3x. If the total area is 28 m², find the value of x by solving the quadratic equation.

Answer: x = 4

Question 2: A student has a quadratic equation x² + 7x + 12 = 0. They claim the solutions are x = -3 and x = -4. Verify this by factorising the quadratic and explain any mistake if present.

Answer: Correct solutions are x = -3 or x = -4

Question 1: A ball is thrown upwards with an initial velocity such that its height after t seconds is given by h = -5t² + 20t + 2. Find the times when the ball reaches its maximum height and when it hits the ground.

Answer: t = 2 seconds when max height; t ≈ 4.2 seconds when hitting ground

Question 1: Solve the quadratic x² - 6x + 9 = 0 by factorising. Then, verify the solution by expanding the factors.

Answer: x = 3

Question 2: Given the quadratic x² + 4x - 5 = 0, factorise and solve for x. Confirm your solutions by expansion.

Answer: x = 1 or x = -5

Question 1: Complete the factorisation of x² + 2x - 8 = 0 and solve for x.

Answer: x = 2 or x = -4

Question 2: Identify the mistake in solving x² + 7x + 10 = 0 by incorrectly factoring as (x + 5)(x + 2) = 0 when the solutions are x = -5 and x = -2. Is this correct?

Answer: Yes, the factorisation is correct and solutions are x = -5, -2

Question 1: A student solves x² + 4x + 4 = 0 by writing (x + 2)² = 0 and concludes x = 2. Explain what mistake was made and find the correct solution.

Answer: Incorrect: x = 2; Correct: x = -2