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Lesson 10 of 16

    Factorising quadratics of the form ax^2 + bx + c

    I can factorise quadratics of the form ax^2 + bx + c.

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    Lesson 10 of 16
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      Factorising quadratics of the form ax^2 + bx + c

      I can factorise quadratics of the form ax^2 + bx + c.

      Lesson details

      Key learning points

      1. For these cases, there are restrictions on how you decompose the x term.
      2. Using the area model can show why this is.
      3. By considering the structure, you can deduce how to decompose the x term.

      Keywords

      • Factorise - To factorise is to express a term as the product of its factors.

      • Quadratic - A quadratic is an equation, graph, or sequence whereby the highest exponent of the variable is 2

      Common misconception

      Believing the constants in the binomials must sum to the coefficient of x and multiply to the constant in the quadratic.

      Use an area model to show what is happening when the coefficient of x^2 is not 1. Pupils should always check their answers by expanding.

      The second learning cycle contains a proof for why the 'ac' method for decomposing the x term works. Pupils need to be confident using the distributivity method to factorise quadratics of the form x^2 + bx + c first before being introduced to this proof.
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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      Prior knowledge starter quiz

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      6 Questions

      Q1.
      Factorise the expression: $$x^2 - x - 6$$

      Correct Answer: (x - 3)(x + 2), (x + 2)(x - 3)

      Q2.
      Factorise the expression: $$x^2 + 9x +20$$

      Correct Answer: (x + 4)(x + 5), (x + 5)(x + 4)

      Q3.
      Factorise the expression: $$x^2 - 4x + 4$$

      Correct Answer: (x-2)(x-2), (x-2)^2

      Q4.
      Factorise the expression: $$x^2 - 25$$

      Correct Answer: (x - 5)(x + 5), (x + 5)(x - 5)

      Q5.
      Factorise this expression: $$x^2 - 6x + 9$$

      Correct answer: $$(x - 3)^2$$
      $$(x - 3)(x + 3)$$
      $$(x+9)(x-1)$$

      Q6.
      Factorise the expression: $$x^2 + 6x + 9$$

      $$(x + 9)(x - 9)$$
      Correct answer: $$(x + 3)^2$$
      $$(x+2)(x+3)$$

      Assessment exit quiz

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      6 Questions

      Q1.
      Factorise the expression $$4x^2 - 4x - 15$$

      Correct Answer: (2x + 3)(2x - 5), (2x - 5)(2x + 3)

      Q2.
      Factorise the expression $$3x^2 + 2x - 8$$

      Correct Answer: (3x - 4)(x + 2), (x + 2)(3x - 4)

      Q3.
      Factorise the expression $$6x^2 - 5x - 6$$

      Correct Answer: (3x + 2)(2x - 3), (2x - 3)(3x + 2)

      Q4.
      Factorise the expression $$5x^2 + 13x + 6$$

      Correct Answer: (x + 2)(5x + 3), (5x + 3)(x + 2)

      Q5.
      Factorise the expression $$2x^2 - x - 15$$

      Correct Answer: (x - 3)(2x + 5), (2x + 5)(x - 3)

      Q6.
      Factorise the expression $$7x^2 + 42x - 49$$

      Correct Answer: (x + 7)(7x - 7), (7x - 7)(x + 7), 7(x+7)(x-1), 7(x-1)(x+7)

      Lesson appears in

      UnitMaths / Algebraic manipulation

      Maths

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