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 - 4x = 0.

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

  2. Solve x squared - 9x + 18 = 0.

    • 3 and 6
    • 3 and -6
    • -3 and 6
    • -3 and -6

  3. The solutions of 2x squared = 14x are x = 7 and x = 0.

    Circle one:   True   False

  4. If (x - 4)(x + 1) = 0, what are the two solutions?

    • x = -4 or x = 1
    • x = 4 or x = 1
    • x = 4 or x = -1
    • x = -4 or x = -1

  5. Solve 5x squared = 30x. What is the non-zero solution?

    Answer: ______________

  6. The zero product rule says a product is zero only when at least one of its factors is zero.

    Circle one:   True   False

  7. Tom solves x squared - 6x + 8 = 0. He factorises to (x - 2)(x - 4) = 0, then writes x - 2 = x - 4 and concludes there is no solution. What went wrong?

    • He set the two factors equal to each other instead of setting each to zero
    • The factorisation should have been (x + 2)(x + 4)
    • x squared - 6x + 8 has no real solutions
    • He should have divided both sides by x

  8. Solve 2x squared + 5x + 2 = 0. What is the sum of the two solutions?

    Answer: ______________

  9. Ravi solves 2x squared - 8x = 0 by dividing both sides by 2x and gets x = 4. Which solution did he lose?

    • x = -4
    • x = 8
    • x = 0
    • No solution was lost

  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
LightMySky · lightmysky.comW1-mt_tg_sqRzDjU-s1

Answer key

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

Solving Quadratic Equations by Factorising W1-mt_tg_sqRzDjU-s1

  1. 0 and 4 · Take out the common factor x to get x(x - 4) = 0, so x = 0 or x = 4.
  2. 3 and 6 · The pair -3 and -6 multiplies to 18 and adds to -9, so (x - 3)(x - 6) = 0 gives x = 3 or x = 6.
  3. True · Rearrange to 2x squared - 14x = 0, factorise to 2x(x - 7) = 0, and the rule gives x = 0 or x = 7.
  4. x = 4 or x = -1 · Set each factor to zero: x - 4 = 0 gives x = 4, and x + 1 = 0 gives x = -1.
  5. 6 · Rearrange to 5x squared - 30x = 0, factorise to 5x(x - 6) = 0, and the solutions are 0 and 6.
  6. True · If A times B = 0, then A = 0 or B = 0, and there is no other case.
  7. He set the two factors equal to each other instead of setting each to zero · His factorisation is right. The rule says each factor equals zero, not that the factors equal each other, so x = 2 or x = 4.
  8. -2.5 · Splitting the middle term gives (2x + 1)(x + 2) = 0, so the solutions are -1/2 and -2, and their sum is -2.5.
  9. x = 0 · Factorising gives 2x(x - 4) = 0, so x = 0 or x = 4. Dividing by 2x assumed x was not zero, so x = 0 was lost.
  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