#19
Top 50 Mistake
Not taking out the highest common factor
"The Partial Factor"
The Mistake in Action
Factorise fully: $12x + 18$
Wrong: $2(6x + 9)$
Why It Happens
Students find a common factor but not the highest common factor. They stop too early.
The Fix
Always check if you can factor further!
$2(6x + 9)$ — Can we factor 6x + 9? Yes! Both are divisible by 3.
Better approach: Find the HCF of 12 and 18 first.
- HCF = 6
$$12x + 18 = 6(2x + 3)$$
Check: $6 \times 2x = 12x$ ✓, $6 \times 3 = 18$ ✓
Spot the Mistake
Can you identify where this student went wrong?
Factorise fully: $12x + 18$
$= 2(6x + 9)$
Click on the line that contains the error.
Related Topics
Learn more about the underlying maths: