Factorise the polynomial by the method of completing the square.
$p^{2} + 6 p - 16$

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Solution

$p^{2} + 6 p - 16 = 0$

$p^{2} + 6 p = 16$

thrid term = $(\frac{1}{2} \times$ coefficient of $p)^{2}$

$= (\frac{1}{2} \times 6)^{2} = 9$

Adding $9$ on both sides

$p^{2} + 6 p + 9 = 16 + 9$

$(p + 3)^{2} = 25$

Taking square root,

$p + 3 = \sqrt{25}$

$p + 3 = + 5$ OR $p + 3 = - 5$

$p = 2$ OR $p = - 8$

Thus , $p^{2} + 6 p - 16 = (p - 2) (p + 8)$

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