# A4c – Factorising (basic)

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# Factorising involving a single set of brackets

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Given that $$x$$ is a positive integer, explain why $$3x+21$$ cannot be prime.

Given that $$n$$ is positive integer, decide whether each of the following is true or false:
1.  4 must be a factor of $$4n+12$$
2.  8 cannot be a factor of $$4n+12$$
3.  5 cannot be a factor of $$4n+12$$
4.  $$8n+12$$ must be a multiple of $$4n+12$$
5.  $$8n+24$$ must be a multiple of $$4n+12$$
6.  The highest common factor of $$(5n+15)$$ and $$(4n+12)$$ must be greater than 1
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