Question: Factorise:
q2 − 10q + 21
Solution:
The given expression is $q^{2}-10 q+21$.
Find two numbers that follow the conditions given below:
Sum $=-10$
Product $=21$
Clearly, the numbers are $-7$ and $-3$.
$q^{2}-10 q+21=q^{2}-7 q-3 q+21$
$=q(q-7)-3(q-7)$
$=(q-7)(q-3)$
