Question
Factor polynomial $$ -a^{6}+a $$
Answer
$$ -a^{6}+a = a( -a+1 )( a^{4}+a^{3}+a^{2}+a+1 ) $$
Explanation
Step 1 :
After factoring out $ a $ we have:
$$ -a^{6}+a = a ( -a^{5}+1 ) $$Step 2 :
To factor $ -a^{5}+1 $ we can use formula:
$$ I^5 - II^5 = (I - II)(I^4 + I^3 \cdot II + I^2 \cdot II^2 + I \cdot II^3 + II^4) $$After putting $ I = 1 $ and $ II = a $ , we have:
$$ -a^{5}+1 = ( -a+1 ) ( a^{4}+a^{3}+a^{2}+a+1 ) $$This page was created using
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