Factorising Quadratics with a Leading Coefficient · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Factorising Quadratics with a Leading Coefficient

Mathematics · Algebra · ages 14-15
Name ______________________   Date ____________

  1. 5x squared + 3x factorises to x(5x + 3).

    Circle one:   True   False

  2. Factorise 2x squared + 6x + 4.

    • 2(x + 1)(x + 2)
    • (x + 1)(x + 2)
    • 2(x + 3)(x + 2)

  3. After splitting 4x squared + 13x + 3 into 4x squared + 12x + x + 3, what is the factorisation?

    • (4x + 3)(x + 1)
    • (2x + 1)(2x + 3)
    • (4x + 2)(x + 3)
    • (4x + 1)(x + 3)

  4. For 2x squared + 5x + 3, the pair multiplies to 6 and adds to 5. Which pair is it?

    • 3 and 2
    • 6 and 1
    • 5 and 1

  5. Factorise 3x squared + 5x + 2.

    • (3x + 1)(x + 2)
    • (3x + 2)(3x + 1)
    • (3x + 2)(x + 1)

  6. In 3x squared + 7x + 2, the pair for the split is 6 and 1.

    Circle one:   True   False

  7. Which quadratic does (2x + 3)(4x + 1) expand to?

    • 8x squared + 14x + 3
    • 8x squared + 12x + 3
    • 6x squared + 4x + 3

  8. 4x squared + 4x + 1 is a perfect square, (2x + 1) squared.

    Circle one:   True   False

  9. Factorise 2x squared - 3x - 2 as (2x + a)(x + b). What is a times b?

    Answer: ______________

  10. Factorise 12x squared + 5x - 2.

    • (4x + 2)(3x - 1)
    • (12x - 1)(x + 2)
    • (4x - 1)(3x + 2)
    • (4x - 2)(3x + 1)
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Answer key

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Factorising Quadratics with a Leading Coefficient W1-mt_IdKGCzbH07-s1

  1. True · Both terms share a factor of x, so taking it out gives x(5x + 3).
  2. 2(x + 1)(x + 2) · Take out 2 to get 2(x squared + 3x + 2), and the inside factorises to (x + 1)(x + 2).
  3. (4x + 1)(x + 3) · Group as 4x(x + 3) + 1(x + 3), then take out the common bracket (x + 3) to get (4x + 1)(x + 3).
  4. 3 and 2 · 3 and 2 multiply to 6 and add to 5, so the middle term 5x splits into 3x and 2x.
  5. (3x + 2)(x + 1) · The product is 6 and the pair 3 and 2 adds to 5, so the split 3x squared + 3x + 2x + 2 groups to (3x + 2)(x + 1).
  6. True · The product a times c is 6, and 6 and 1 multiply to 6 and add to 7.
  7. 8x squared + 14x + 3 · The cross terms are 2x and 12x, which collect to 14x, and the constant is 3.
  8. True · The product is 4 and the pair 2 and 2 adds to 4, so the split groups to (2x + 1)(2x + 1).
  9. -2 · The factorisation is (2x + 1)(x - 2), so a = 1, b = -2, and a times b = -2.
  10. (4x - 1)(3x + 2) · The product is -24, and the pair 8 and -3 adds to 5, so the split 12x squared + 8x - 3x - 2 groups to (4x - 1)(3x + 2).
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