★ Must-know
📌 A factorisation is complete only when all common factors have been taken outside the brackets.
Further detail
1. A student changes into . Which operation has the student performed?
2. A student writes . What change is needed to make the factorisation complete?
3. To factorise by grouping, which sequence should be used?
What does factorising do to an expression?
It writes the expression as a product of factors by taking out common factors.
When is a factorisation complete?
When all common factors have been taken outside the brackets.
What is the sequence for factorising by grouping?
Pair terms with common factors, factor each pair, then take out the common bracket.
How do you factor a monic quadratic using two numbers?
Find numbers with product and sum , then use them as the factor constants.
For with , what product and sum guide the split-middle-term method?
The two numbers have product and sum .
After splitting the middle term in , what does the grouping method factor out?
The common bracket.
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