Factorise $x^{2} + 5 x + 4$

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Solution

Using identity $(x + a) (x + b) = x^{2} + (a + b) x + a b$
Thus $x^{2} + 5 x + 4$
$= x^{2} + 4 x + x + 4$
$= x (x + 4) + 1 (x + 4)$
$= (x + 4) (x + 1)$

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