Question
Factor polynomial $$ 256x^{2}-96x+9 $$
Answer
$$ 256x^{2}-96x+9 = ( 16x-3 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ 256x^2 = \left( \color{blue}{ 16x } \right)^2 ~~ \text{and} ~~ 9 = \left( \color{red}{ 3 } \right)^2 $$The middle term ( $ -96x $ ) is two times the product of the terms that are squared.
$$ -96x = - 2 \cdot \color{blue}{16x} \cdot \color{red}{3} $$We can conclude that the polynomial $ 256x^{2}-96x+9 $ is a perfect square trinomial, so we will use the formula below.
$$ A^2 - 2AB + B^2 = (A - B)^2 $$In this example we have $ \color{blue}{ A = 16x } $ and $ \color{red}{ B = 3 } $ so,
$$ 256x^{2}-96x+9 = ( \color{blue}{ 16x } - \color{red}{ 3 } )^2 $$This page was created using
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