Factor polynomial $$ -c^{10}+16c^{2} $$
Answer
$$ -c^{10}+16c^{2} = c^{2}( -c^{2}+2 )( c^{2}+2 )( c^{4}+4 ) $$
Explanation
Step 1 :
After factoring out $ c^{2} $ we have:
$$ -c^{10}+16c^{2} = c^{2} ( -c^{8}+16 ) $$Step 2 :
Rewrite $ -c^{8}+16 $ as:
$$ -c^{8}+16 = 16 -x^8 = (4)^2 - (c^{4})^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 4 $ and $ II = c^{4} $ , we have:
$$ -c^{8}+16 = (4)^2 - (c^{4})^2 = ( -c^{4}+4 ) ( c^{4}+4 ) $$Step 3 :
Rewrite $ -c^{4}+4 $ as:
$$ -c^{4}+4 = 4 -x^4 = (2)^2 - (c^{2})^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = 2 $ and $ II = c^{2} $ , we have:
$$ -c^{4}+4 = (2)^2 - (c^{2})^2 = ( -c^{2}+2 ) ( c^{2}+2 ) $$This page was created using
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