If the factorized form of $p (x) = 25 x^{2} - 40 x + 16$ is $(5 x - m)^{2}$ . Find $m$ .

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Solution

$p (x) = 25 x^{2} - 40 x + 16$
$= 25 x^{2} - 20 x - 20 x + 16$
$= 5 x (5 x - 4) - 4 (5 x - 4)$
$= {(5 x - 4)}^{2} .$
Comparing with ${(5 x - m)}^{2}$
$\Rightarrow m = 4$
Hence, the answer is $4.$

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