Complete Factorisation of Polynomials

Questions asking to factorise a polynomial completely into linear and/or irreducible quadratic factors, often using the factor theorem or inspection.

3 questions · Moderate -0.6

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OCR MEI C1 Q4

3 marks Standard +0.3

4 Factorise \(n ^ { 3 } + 3 n ^ { 2 } + 2 n\). Hence prove that, when \(n\) is a positive integer, \(n ^ { 3 } + 3 n ^ { 2 } + 2 n\) is always divisible by 6 .

Edexcel C1 2008 June Q2

3 marks Easy -1.8

Factorise completely $$x ^ { 3 } - 9 x .$$

OCR MEI C1 2011 June Q10

3 marks Moderate -0.3

10 Factorise \(n ^ { 3 } + 3 n ^ { 2 } + 2 n\). Hence prove that, when \(n\) is a positive integer, \(n ^ { 3 } + 3 n ^ { 2 } + 2 n\) is always divisible by 6 .