Coaching Centre
Factorising expressions
Factorising algebraic expressions by taking out the highest common factor, including negative and pronumeral factors.
Taking out the HCF
Factorise $12x + 18$.
HCF $= 6$.
$6(2x + 3)$
Factorise $15a^2b - 10ab$.
HCF of $15$ and $10$ is $5$; both terms contain $a$ and $b$. HCF $= 5ab$.
$5ab(3a - 2)$
Factorise $-4x - 8$.
Take out $-4$ so the first term inside is positive.
$-4(x + 2)$
Factorise $5x + 20$
$5(x + 4)$
Factorise $x^2 + 7x$
$x(x + 7)$
Check a factorisation
Expand it.
Factorise $12x + 18$.
HCF $6$.
Factorise $15a^2b - 10ab$.
HCF $5ab$.
Factorise $-4x - 8$.
Take out $-4$.
Factorise $5x + 20$.
HCF $5$.
Factorise $x^2 + 7x$.
HCF $x$.
Factorise $3m^2 - 12m$.
HCF $3m$.
Which is fully factorised?
$8y + 12$ has HCF $4$.
Factorise $14 - 7p$.
HCF $7$.
New numbers every time. Keep going until you get five in a row.