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Factorising Calculator

Factorise expressions the two ways GCSE asks: pull out the highest common factor, or split a quadratic into double brackets by finding the pair of numbers that multiply to c and add to b. The search for that pair is shown, and every answer is expanded back out as a check.

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    Worked Example

    Factorise x² + 5x + 6.

    1. Two numbers that multiply to 6 and add to 5: 2 and 3
    2. So x² + 5x + 6 = (x + 2)(x + 3)
    3. Check:2x + 3x = 5x, and 2 × 3 = 6 ✓

    Answer: (x + 2)(x + 3)

    Try These Yourself

    Factorise 8x + 12.Show answerHide answer

    Answer: 4(2x + 3)

    The HCF of 8 and 12 is 4.

    Factorise x² − x − 12.Show answerHide answer

    Answer: (x − 4)(x + 3)

    −4 × 3 = −12 and −4 + 3 = −1.

    Factorise x² − 9.Show answerHide answer

    Answer: (x − 3)(x + 3)

    Difference of two squares: −3 and 3 multiply to −9, add to 0.