Factorising Expressions · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Factorising by Taking Out a Common Factor

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

  1. Factorise 6x + 9 by taking out the common factor.

    • 3(2x + 3)
    • 2(3x + 9)
    • 6(x + 9)
    • 3(2x + 9)

  2. What is the highest common factor of the two terms in 6x + 9?

    • 3
    • 6
    • 9
    • x

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

    • 2
    • 4
    • 24

  4. True or false: in the expression 4x + 6, the highest common factor of the two terms is 2.

    Circle one:   True   False

  5. Factorise 12y + 8. What number goes in front of the bracket?

    Answer: ______________

  6. Ben factorised 12x + 18 as 6(2x + 3). How can he check this is correct?

    • Expand 6(2x + 3) and see if he gets 12x + 18 back
    • Divide 12x + 18 by 2 and compare
    • Add 6 to both sides of the expression

  7. Factorise 10a + 15.

    • 5(2a + 3)
    • 2(5a + 15)
    • 10(a + 15)
    • 5(2a + 15)

  8. Factorise 14m + 21.

    • 7(2m + 3)
    • 2(7m + 21)
    • 14(m + 21)
    • 7(2m + 7)

  9. Maya factorised 8x + 20 as 2(4x + 10). Is she finished?

    • Yes, this is fully factorised
    • No, she should have used 8 instead of 2
    • No, 2 is still a common factor of 4x and 10 inside the bracket

  10. What is the highest common factor of 18 and 24?

    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. 3(2x + 3) · The HCF of 6x and 9 is 3, and dividing each term by 3 leaves 2x and 3, so the answer is 3(2x + 3).
  2. 3 · The biggest number that divides both 6 and 9 is 3, and x is not part of the 9, so the HCF is 3.
  3. 4 · 4 is the biggest number that divides both 8 and 12 exactly. 24 is a common multiple, not a common factor.
  4. True · 2 divides both 4 and 6 exactly, and no bigger number does.
  5. 4 · The HCF of 12 and 8 is 4, so 4 is the number that goes in front: 4(3y + 2).
  6. Expand 6(2x + 3) and see if he gets 12x + 18 back · Expanding the bracket should recreate the original expression. 6(2x + 3) equals 12x + 18, so it checks out.
  7. 5(2a + 3) · The HCF of 10 and 15 is 5. Dividing gives 10a divided by 5 is 2a, and 15 divided by 5 is 3, so the answer is 5(2a + 3).
  8. 7(2m + 3) · The HCF of 14 and 21 is 7. That gives 14m divided by 7 is 2m, and 21 divided by 7 is 3, so the answer is 7(2m + 3).
  9. No, 2 is still a common factor of 4x and 10 inside the bracket · 2 does divide both terms, but it isn't the highest common factor. 8 and 20 also divide by 4, giving the fully factorised form 4(2x + 5).
  10. 6 · The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The biggest shared one is 6.
Worksheet · LightMySky