Factor polynomial $$ x^{10}-49x^{2} $$
Answer
$$ x^{10}-49x^{2} = x^{2}( x^{4}-7 )( x^{4}+7 ) $$
Explanation
Step 1 :
After factoring out $ x^{2} $ we have:
$$ x^{10}-49x^{2} = x^{2} ( x^{8}-49 ) $$Step 2 :
Rewrite $ x^{8}-49 $ as:
$$ x^{8}-49 = (x^{4})^2 - (7)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = x^{4} $ and $ II = 7 $ , we have:
$$ x^{8}-49 = (x^{4})^2 - (7)^2 = ( x^{4}-7 ) ( x^{4}+7 ) $$This page was created using
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