Factorising by Quadratic Trinomials & Grouping

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Last updated 8:44 AM on 6/16/26
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4 Terms

1
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How to factorise using Grouping (4 Terms)

  • Group the expression into two pairs, then factor each pair.

  • Steps:

    1. Group two terms and another two terms that have a common factor.

    2. Factor each group.

    3. If both groups have a common bracket, factor it out.

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2ab + 4a + 3b + 6

  1. Group: 2ab+4a+3b+6

  2. Factor each:

    • = 2a(b + 2) + 3(b + 2)

  3. Common factor is the whole bracket, so BRACKtorise! (b + 2)

    • = (b + 2)(2a + 3) 

  • Final Answer:

    • (b + 2)(2a + 3)

3
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How to factorise using Quadratic Trinomials (Type x² + bx + c)

  • A quadratic trinomial has three terms, typically starting with an x² term. To factorise x² + bx + c, you need to find two numbers that:

    1. Multiply to give the constant term 'c'.

    2. Add to give the coefficient of the x term, 'b'. The factorised form will be (x + first number)(x + second number). Always check for an HCF first!

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a² − 5a − 14

  1. Check for HCF: None.

  2. Identify b and c: In a² − 5a − 14,

    • b = −5

    • c = −14

  3. Find two numbers that:

    • Multiply to give −14.

    • Add to give −5.

  4. Consider factors of -14:

    • 1 and -14 (sum = -13)

    • -1 and 14 (sum = 13)

    • 2 and -7 (sum = -5) <-- These are our numbers!

    • -2 and 7 (sum = 5)

  5. Write the factors: The numbers are +2 and −7. (a + 2)(a − 7)

  6. Check (by expanding): (a + 2)(a − 7) = a² − 7a + 2a − 14 = a² − 5a − 14. Correct!