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Factorisation by Common Factors

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Question

Find the factors of the polynomial given below.
$2 m^{2} + 5 m + 3$

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Solution

$2 m^{2} + 5 m + 3$
$= 2 m^{2} + 2 m + 3 m + 3$
$= 2 m (m + 1) + 3 (m + 1)$
$= (2 m + 3) (m + 1)$
$∴$ The factors are $(2 m + 3)$ and $(m + 1)$

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