Factorising Expressions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Factorising by Taking Out a Common Factor

Mathematics · Algebra · ages 12-13
Name ______________________   Date ____________

  1. Factorise 5t + 20 by taking out its HCF.

    • 5(t + 20)
    • 5(5t + 4)
    • 5(t + 4)
    • t(5 + 20)

  2. Why is x not a common factor of the terms in 7x + 14?

    • The coefficient 7 is an odd number.
    • The term 14 has no factor x.
    • The expression contains two terms.
    • The coefficient of x is not 1.

  3. What is the highest common factor (HCF) of 8 and 12?

    • 2
    • 4
    • 24

  4. True or false: the HCF of the terms in 4x + 6 is 2.

    Circle one:   True   False

  5. Taking out the HCF gives 8r + 12s - 20 = 4(2r + 3s + k). What is k?

    Answer: ______________

  6. Ben wrote a factorisation as 6(2x + 3). Expand the bracket to check his work. Which expression should he compare with the original?

    • 12x + 3
    • 12x + 18
    • 12x + 108

  7. Factorise 12b - 8 by taking out its positive HCF.

    • 4(3b - 2)
    • 4(3b + 2)
    • 4(3b - 8)
    • 4(12b - 2)

  8. Factorise 6xy + 9y by taking out the HCF.

    • 3(2xy + 3)
    • 3x(2y + 3)
    • y(6x + 3)
    • 3y(2x + 3)

  9. Maya wrote 8x + 20 = 2(4x + 10). Has she taken out the HCF?

    • Yes. Any common factor outside means the HCF has been taken out.
    • No. The largest coefficient, 8, must be the factor outside.
    • No. The terms inside still share a factor of 2.

  10. A factorisation is 18x + c = 6(3x - 4). What value of c makes the expressions equal for every x?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

Factorising by Taking Out a Common Factor W1-mt_uESbzWCZIq-s1

  1. 5(t + 4) · The HCF is 5. Dividing 5t by 5 leaves t, and dividing 20 by 5 leaves 4.
  2. The term 14 has no factor x. · A common factor must occur in every term. The term 7x contains x, but the constant 14 does not.
  3. 4 · Their common factors are 1, 2 and 4. The largest is 4. The number 24 is a common multiple, not a factor of either number.
  4. True · The coefficients share factors 1 and 2. The constant has no x, so the HCF is 2.
  5. -5 · The constant inside is -20 ÷ 4 = -5, so k = -5.
  6. 12x + 18 · Multiply 6 by both terms: 6 × 2x = 12x and 6 × 3 = 18. Compare the expansion, 12x + 18, with the original expression to check the factorisation.
  7. 4(3b - 2) · The HCF is 4. Dividing the signed terms by 4 gives 3b and -2.
  8. 3y(2x + 3) · The coefficients share 3 and both terms contain y. Taking out 3y gives 3y(2x + 3).
  9. No. The terms inside still share a factor of 2. · Her expression is equivalent, but 4x and 10 still share 2. The original HCF is 4, giving 4(2x + 5).
  10. -24 · Expanding gives 18x - 24, so c = -24.
Worksheet · LightMySky