Checking and securing understanding of factorising | Maths

Starter quiz

A bakery sells $x$ cakes for £2.25 each. If the cost to make each cake is £1.20, what is the profit, $p$ , for selling all the cakes?

$p = 1.2x$

$p = (2.25-1.2)x$ ✓

$p = 2.25x - 1.2$
What is the value of $x$ in $2x + 3 = 15$

'6' ✓
Simplify $3ax + 9ax + 13ax + b$

'25ax + b' ✓
Expand $2(x - 3) + 4(2x + 1)$ and simplify where possible.

'10x - 2' ✓
Simplify $3(x + 2)^2 - (x - 1)(x + 1)$ where possible.

$2x^2 + 12x + 13$ ✓

$3x^2 + 12x + 7$

$4x^2 + 12x + 7$
Factorise $4x^2 - 16$ completely.

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

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

$4(x-2)(x+2)$ ✓

Exit quiz

Fully factorise the expression $5x + 20$

$5(x + 4)$ ✓

$x(5 + 20)$

$25(x + 4)$

$5(x - 4)$
Fully factorise the expression $3y^2 + 12y$

$3y(y^2 + 4)$

$15y(y + 4)$

$3(y^2 + 4)$

$3y(y + 4)$ ✓
Fully factorise the expression $4z - 8z^2$

$-4z(z - 1)$

$4z(1 - 2z)$ ✓

$12z(1 - 2z)$

$-8z(z - 2)$
Fully factorise the expression $6m^2 + 24m + 18$

$2(3m^2 + 12m + 9)$

$6(m^2 + 4m + 3)$ ✓

$6(m + 2)^2$

$6(m + 3)(m + 1)$
Fully factorise the expression $8x^2 - 20x + 12$ .

$8(x^2 - 2.5x + 1.5)$

$2(4x^2 - 10x + 6)$

$4(2x^2 - 5x + 3)$ ✓

$2(2x - 3)(2x - 2)$
Fully factorise the expression $7y^2 - 14y$ .

$7y(y - 2)$ ✓

$7(y^2 - 2)$

$14y(y - 1)$

$7(y - 2)(y + 2)$

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Lesson Details

Key learning points

An expression can be described as being factorised.
An expression is fully factorised if the highest common factor has been taken out.
The distributive law can help us factorise an expression.

Common misconception

Leaving answers which are not fully factorised when they are required to.

There should be a focus on reading questions to decipher what they are being asked to do. When they have to fully factorise they need the highest common factor of all the terms. LC3 focuses on situations where they are not going to fully factorise.

Keywords

Factor - A factor is a term which exactly divides another term.
Factorise - To factorise is to express a term as the product of its factors.