Solving quadratic equations by factorising · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Solving quadratic equations by factorising

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

  1. Solve x squared + x - 6 = 0. What is the sum of the two solutions?

    Answer: ______________

  2. If the product of two numbers is zero, at least one of the numbers must be zero.

    Circle one:   True   False

  3. Solve x squared - 4x = 0.

    • 4 only
    • 0 and -4
    • -4 only
    • 0 and 4

  4. Which rearrangement of x² + 5x = 14 prepares it for the zero product rule?

    • x² + 5x - 14 = 0
    • x² + 5x + 14 = 0
    • x² - 5x - 14 = 0
    • x² + 14x - 5 = 0

  5. Solve x squared + 4x - 21 = 0. What is the larger solution?

    Answer: ______________

  6. Solve x squared - 5x - 14 = 0.

    • 7 and 2
    • -7 and -2
    • -7 and 2
    • 7 and -2

  7. An equation has solutions x = 1 and x = -6. Which equation could it be?

    • x squared - 5x - 6 = 0
    • x squared + 5x + 6 = 0
    • x squared - 5x + 6 = 0
    • x squared + 5x - 6 = 0

  8. A garden-length calculation gives candidate values 6 metres and -4 metres. Both can be kept as possible garden lengths.

    Circle one:   True   False

  9. Which values of x satisfy x squared = 7x - 10?

    • 2 and -5
    • 2 and 5
    • 7 and 10
    • -2 and -5

  10. A garden has width x metres and length (x + 5) metres, and its area is 84 square metres. What is the width?

    • 12 metres
    • 7 metres
    • -7 metres
    • -12 metres
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Answer key

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Solving quadratic equations by factorising W1-mt_tg_sqRzDjU-s1

  1. -1 · The factorisation is (x + 3)(x - 2) = 0, so the solutions are -3 and 2, and their sum is -1.
  2. True · A product is zero only when one of its factors is zero.
  3. 0 and 4 · Take out the common factor x to get x(x - 4) = 0, so x = 0 or x = 4.
  4. x² + 5x - 14 = 0 · Subtract 14 from both sides. After factorising the left side, its product will equal zero.
  5. 3 · The factorisation is (x + 7)(x - 3) = 0, so the solutions are -7 and 3, and the larger is 3.
  6. 7 and -2 · The pair -7 and 2 multiplies to -14 and adds to -5, so (x - 7)(x + 2) = 0 gives x = 7 or x = -2.
  7. x squared + 5x - 6 = 0 · Solutions 1 and -6 mean the brackets are (x - 1) and (x + 6), which expand to x squared + 5x - 6.
  8. False · A garden length must be positive. Keep 6 metres and reject -4 metres.
  9. 2 and 5 · Rearrange to x squared - 7x + 10 = 0, factorise to (x - 2)(x - 5) = 0, so x = 2 or x = 5.
  10. 7 metres · The area gives x(x + 5) = 84, so (x + 12)(x - 7) = 0, and x = -12 or x = 7. A width cannot be negative.
Worksheet · LightMySky