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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:

- 4 must be a factor of \(4n+12\)
- 8 cannot be a factor of \(4n+12\)
- 5 cannot be a factor of \(4n+12\)
- \(8n+12\) must be a multiple of \(4n+12\)
- \(8n+24\) must be a multiple of \(4n+12\)
- The highest common factor of \((5n+15)\) and \((4n+12)\) must be greater than 1

- True
- False
- False
- False
- True
- True

Teacher resources

**Teachers**: log in to access the following:

- Worksheet (with space for student work)
- Handout (slides with exercises only; 4 per page for reduced printing)

- Skills drill worksheet (40 questions on one side of A4; answers included)

Links to past exam questions

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