Solve: p^2+6 p-16 - Vidyadip

Question

Solve:
$p^2+6 p-16$

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Answer

$p^2+6 p-16$
$p^2+6 p+\left(\frac{6}{2}\right)^2-\left(\frac{6}{2}\right)^2-16\left[\text { Adding and suobtrating }\left(\frac{6}{2}\right)^2, \text { that is } 3^2\right]$
$=p^2+6 p+3^2-9-16$
$=(p-3)^2-25[\text { completing the square }]$
$=(p+3)^2-5^2$
$=[(p+3)-5][(p+3)+5]$
$=(p+3-5)(p+3+5)$
$=(p-2)(p+8)$

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