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Year 10
Foundation

Factorising a quadratic expression

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

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Year 10
Foundation

Factorising a quadratic expression

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

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Lesson details

Key learning points

  1. The distributive law can be used to find the two factors of a quadratic expression with three non-zero terms.
  2. An area model can be used to explore the underlying structure.
  3. You can check your factors by finding the product and checking it against the quadratic.

Keywords

  • Factorise - 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

Pupils often get signs the incorrect way round in the binomials. E.g. (x+2)(x-4) instead of (x-2)(x+4)

Encourage pupils to always expand their binomials to check they are correct. Using representations such as an area model should reduce the likelihood of this as pupils focus on the structure and reason behind their choices.


To help you plan your year 10 maths lesson on: Factorising a quadratic expression, download all teaching resources for free and adapt to suit your pupils' needs...

When using algebra tiles to factorise, pupils should be confident with why their algebra tiles need to make a rectangle. Using axes can help pupils see where negative algebra tiles should go and the benefit of zero pairs.
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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).

Lesson video

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Starter quiz

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6 Questions

Q1.
Expand and simplify the expression: $$3(y - 2)(y + 4)$$
Correct answer: $$3y^2 + 6y - 24$$
$$3y^2 - 6y + 8$$
$$3y^2 + 12y - 8$$
Q2.
Expand and simplify the expression: $$(y^2 + 3y - 4)(2y - 1)$$
$$2y^3 + 6y^2 - 8y - 4$$
Correct answer: $$2y^3 + 5y^2 - 11y + 4$$
$$y^3 + 3y^2 - 4y - 1$$
Q3.
Expand and simplify the expression: $$4(y + 3)(2y - 3)$$
$$4y^2 + 12y - 36$$
$$8y^2 - 12y + 36$$
Correct answer: $$8y^2 + 12y - 36$$
Q4.
Expand and simplify the expression: $$(x + 2)(x - 3)(x + 4)$$
Correct answer: $$x^3 + 3x^2 - 10x - 24$$
$$x^3 + 3x^2 - 10x + 24$$
$$x^3 - 3x^2 - 10x - 24$$
Q5.
Expand and simplify the expression: $$(2x + 1)(x - 5)(x + 3)$$
$$2x^3 - 3x^2 + 32x - 15$$
Correct answer: $$2x^3 - 3x^2 - 32x - 15$$
$$2x^3 + 3x^2 - 32x + 15$$
Q6.
Expand and simplify the expression: $$(x - 2)(3x + 4)(x - 1)$$
Correct answer: $$3x^3 - 5x^2 - 6x + 8$$
$$3x^3 + 5x^2 - 6x - 8$$
$$3x^3 - 5x^2 + 6x - 8$$

Exit quiz

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6 Questions

Q1.
Factorise $$x^2 + 5x + 6$$
Correct answer: $$(x + 2)(x + 3)$$
$$(x - 2)(x - 3)$$
$$(x + 6)(x - 1)$$
Q2.
Factorise $$x^2 + 9x + 20$$
$$(x + 20)(x + 1)$$
$$(x - 5)(x - 4)$$
Correct answer: $$(x + 5)(x + 4)$$
Q3.
Factorise $$x^2 - x - 12$$
$$(x + 4)(x - 3)$$
Correct answer: $$(x - 4)(x + 3)$$
$$(x - 12)(x + 1)$$
Q4.
Factorise $$x^2 + 6x + 8$$
$$(x + 8)(x - 1)$$
$$(x - 2)(x - 4)$$
Correct answer: $$(x + 2)(x + 4)$$
Q5.
Factorise $$x^2 - 10x + 24$$
Correct answer: $$(x - 6)(x - 4)$$
$$(x + 6)(x + 4)$$
$$(x - 24)(x + 1)$$
Q6.
Factorise $$x^2 + 7x + 10$$
$$(x - 5)(x - 2)$$
Correct answer: $$(x + 5)(x + 2)$$
$$(x + 10)(x - 1)$$