1. Factorise the expression 8x + 12.
- A4(2x + 3)
- B2(4x + 6)
- C8(x + 1.5)
- D2(2x + 6)
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Answer: A) 4(2x + 3)
The common factor of 8 and 12 is 4. Dividing each term by 4 gives 2x + 3.
Class 8 Factorisation — practice questions with answers
Algebra · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. What does it mean to factorise an algebraic expression?
- ATo write it as a product of two or more factors
- BTo write it as a sum of two or more terms
- CTo find its numerical value
- DTo remove all the variables from it
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Answer: A) To write it as a product of two or more factors
Factorisation means expressing a given expression as a product of its factors, for example 6x + 9 = 3(2x + 3).
3. Factorise the expression p² - 13p + 36.
- A(p - 4)(p - 9)
- B(p + 4)(p + 9)
- C(p - 6)(p - 6)
- D(p - 4)(p + 9)
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Answer: A) (p - 4)(p - 9)
Two numbers that multiply to 36 and add to -13 are -4 and -9, so p² - 13p + 36 = (p - 4)(p - 9).
4. Factorise the expression x² + 14x + 49.
- A(x + 7)²
- B(x + 14)²
- C(x + 7)(x - 7)
- D(x + 1)(x + 49)
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Answer: A) (x + 7)²
x² + 14x + 49 = x² + 2(x)(7) + 7² = (x + 7)².
5. Factorise the expression x² + 9x + 20.
- A(x + 4)(x + 5)
- B(x + 2)(x + 10)
- C(x + 1)(x + 20)
- D(x + 4)(x - 5)
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Answer: A) (x + 4)(x + 5)
Two numbers that multiply to 20 and add to 9 are 4 and 5, so x² + 9x + 20 = (x + 4)(x + 5).
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