AQA · Mathematics · 8300

GCSE Maths: Quadratics: solving (factorising)

Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Quadratics: solving (factorising) (Corbettmaths Video 266), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.

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  1. What are the solutions to (x − 2)(x + 9) = 0?

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    x = 2 or x = −9. When a product of factors equals zero, at least one factor must be zero.

  2. What are the two roots of (x − 6)(x + 1) = 0?

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    x = 6 and x = −1. Set each factor equal to zero: x − 6 = 0 gives x = 6; x + 1 = 0 gives x = −1.

  3. What are the solutions to x² − 49 = 0?

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    x = 7 or x = −7. This is a difference of squares: x² − 49 = (x − 7)(x + 7) = 0.

  4. If the two solutions to x² + bx + c = 0 are x = −8 and x = −2, what are the values of b and c?

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    b = 10 and c = 16. The factored form is (x + 8)(x + 2) = 0, which expands to x² + 10x + 16 = 0.

  5. If x² + bx + c = 0 has only one solution at x = −3, what are the values of b and c?

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    b = 6 and c = 9. A single solution means a repeated root: (x + 3)(x + 3) = 0, which expands to x² + 6x + 9 = 0.

  6. What are the solutions to (2x − 1)(x − 3) = 0?

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    x = 1/2 or x = 3. Set each factor to zero: 2x − 1 = 0 gives x = 1/2; x − 3 = 0 gives x = 3.

  7. What are the solutions to (4x + 3)(5x − 2) = 0?

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    x = −3/4 or x = 2/5. Set each factor to zero: 4x + 3 = 0 gives x = −3/4; 5x − 2 = 0 gives x = 2/5.

  8. What are the solutions to 4x² − 9 = 0?

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    x = 3/2 or x = −3/2. This is a difference of squares: 4x² − 9 = (2x − 3)(2x + 3) = 0.

  9. When solving a quadratic equation in the form (factor1)(factor2) = 0, apply the ?

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    zero product property

  10. To solve y² − 6y = 27 by factoring, what is the first step?

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    Rearrange to standard form: y² − 6y − 27 = 0. Then factor and solve.

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