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