Factorise: 2a $^{2}$ + 3a + 1. (2 marks)

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Solution

2a $^{2}$ + 3a + 1 = 2a $^{2}$ + 2a + a + 1
= 2a(a + 1) + 1(a + 1) (1 mark)
Use the identity,
$(x + a) (x + b) = x^{2} + (a + b) x + a b$

2a $^{2}$ + 3a + 1 = (a + 1)(2a + 1)
(1 mark)

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