Factor polynomial $$ z^{4}+10z^{2}+25 $$
Answer
$$ z^{4}+10z^{2}+25 = ( z^{2}+5 )^{ 2 } $$
Explanation
Both the first and third terms are perfect squares.
$$ x^4 = \left( \color{blue}{ z^{2} } \right)^2 ~~ \text{and} ~~ 25 = \left( \color{red}{ 5 } \right)^2 $$The middle term ( $ 10x^2 $ ) is two times the product of the terms that are squared.
$$ 10x^2 = 2 \cdot \color{blue}{z^{2}} \cdot \color{red}{5} $$We can conclude that the polynomial $ z^{4}+10z^{2}+25 $ 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 = z^{2} } $ and $ \color{red}{ B = 5 } $ so,
$$ z^{4}+10z^{2}+25 = ( \color{blue}{ z^{2} } + \color{red}{ 5 } )^2 $$This page was created using
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