Factor polynomial $$ x^{6}-256x^{2} $$
Answer
$$ x^{6}-256x^{2} = x^{2}( x-4 )( x+4 )( x^{2}+16 ) $$
Explanation
Step 1 :
After factoring out $ x^{2} $ we have:
$$ x^{6}-256x^{2} = x^{2} ( x^{4}-256 ) $$Step 2 :
Rewrite $ x^{4}-256 $ as:
$$ x^{4}-256 = (x^{2})^2 - (16)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x^{2} $ and $ II = 16 $ , we have:
$$ x^{4}-256 = (x^{2})^2 - (16)^2 = ( x^{2}-16 ) ( x^{2}+16 ) $$Step 3 :
Rewrite $ x^{2}-16 $ as:
$$ x^{2}-16 = (x)^2 - (4)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x $ and $ II = 4 $ , we have:
$$ x^{2}-16 = (x)^2 - (4)^2 = ( x-4 ) ( x+4 ) $$This page was created using
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