Question 1: Factorise the expression 12x + 8. Identify any common factors and explain your steps.

Answer: 4(3x + 2), common factor is 4

Question 2: Determine the mistake in factorising 15x + 10 as 5(3x + 2). Is this correct? Why or why not?

Answer: Yes, it is correct because 5 is the greatest common factor of 15 and 10, and it was correctly factored out.

Question 3: Simplify the expression: 24a + 36b - 18a + 12b.

Answer: 6(4a + 6b - 3a + 2b) = 6(1a + 6b) = 6a + 36b

Question 4: Identify the common factor in 20x² and 15x. Then factorise each expression.

Answer: Common factor is 5x; 20x² = 5x(4x), 15x = 5x(3)

Question 5: A student factors 18x + 24 as 6(3x + 4). Is this correct? Explain any misconception.

Answer: Yes, correct. The common factor is 6, and the expression is correctly factored.

Question 6: Factorise the expression: 35x + 14.

Answer: 7(5x + 2)

Question 7: A common mistake is to factor out only 2 from 10x + 15. Correct or incorrect? Why?

Answer: Incorrect, the greatest common factor is 5, not 2.

Question 8: Solve: Factorise 48x - 36 and verify your answer.

Answer: Common factor is 12; 48x - 36 = 12(4x - 3)

Question 9: Determine and correct the error in this student’s factorisation: 9x + 6 = 3(3x + 2).

Answer: Incorrect, the factor is actually 3, and the factorisation 3(3x + 2) is correct. The error may be in misidentifying the common factor.

Question 10: Express 14x + 21 as a product of its common factors and explain why.

Answer: 7(2x + 3), common factor is 7 because it divides both coefficients evenly.