Factorising a quadratic expression | Maths | Quizalize & Oak National Academy

Starter quiz

Expand and simplify the expression: $3(y - 2)(y + 4)$

$3y^2 + 6y - 24$ ✓

$3y^2 - 6y + 8$

$3y^2 + 12y - 8$
Expand and simplify the expression: $(y^2 + 3y - 4)(2y - 1)$

$2y^3 + 6y^2 - 8y - 4$

$2y^3 + 5y^2 - 11y + 4$ ✓

$y^3 + 3y^2 - 4y - 1$
Expand and simplify the expression: $4(y + 3)(2y - 3)$

$4y^2 + 12y - 36$

$8y^2 - 12y + 36$

$8y^2 + 12y - 36$ ✓
Expand and simplify the expression: $(x + 2)(x - 3)(x + 4)$

$x^3 + 3x^2 - 10x - 24$ ✓

$x^3 + 3x^2 - 10x + 24$

$x^3 - 3x^2 - 10x - 24$
Expand and simplify the expression: $(2x + 1)(x - 5)(x + 3)$

$2x^3 - 3x^2 + 32x - 15$

$2x^3 - 3x^2 - 32x - 15$ ✓

$2x^3 + 3x^2 - 32x + 15$
Expand and simplify the expression: $(x - 2)(3x + 4)(x - 1)$

$3x^3 - 5x^2 - 6x + 8$ ✓

$3x^3 + 5x^2 - 6x - 8$

$3x^3 - 5x^2 + 6x - 8$

Exit quiz

Factorise $x^2 + 5x + 6$

$(x + 2)(x + 3)$ ✓

$(x - 2)(x - 3)$

$(x + 6)(x - 1)$
Factorise $x^2 + 9x + 20$

$(x + 20)(x + 1)$

$(x - 5)(x - 4)$

$(x + 5)(x + 4)$ ✓
Factorise $x^2 - x - 12$

$(x + 4)(x - 3)$

$(x - 4)(x + 3)$ ✓

$(x - 12)(x + 1)$
Factorise $x^2 + 6x + 8$

$(x + 8)(x - 1)$

$(x - 2)(x - 4)$

$(x + 2)(x + 4)$ ✓
Factorise $x^2 - 10x + 24$

$(x - 6)(x - 4)$ ✓

$(x + 6)(x + 4)$

$(x - 24)(x + 1)$
Factorise $x^2 + 7x + 10$

$(x - 5)(x - 2)$

$(x + 5)(x + 2)$ ✓

$(x + 10)(x - 1)$

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

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

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.

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