Factorize:
$\frac{1}{2} x^{2} - 3 x + 4$ .

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Solution

$\frac{1}{2} x^{2} - 3 x + 4$
$= \frac{1}{2} x^{2} - 2 x - x + 4$
$= \frac{1}{2} x (x - 4) - 1 (x - 4)$
$= (x - 4) (\frac{1}{2} x - 1)$
$∴ \frac{1}{2} x^{2} - 3 x + 4 = (x - 4) (\frac{1}{2} x - 1)$

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