Question
Factor polynomial $$ x^{15}+1 $$
Answer
$$ x^{15}+1 = ( x+1 )( x^{4}-x^{3}+x^{2}-x+1 )( x^{10}-x^{5}+1 ) $$
Explanation
Step 1 :
To factor $ x^{15}+1 $ we can use sum of cubes formula:
$$ I^3 - II^3 = (I + II)(I^2 - I \cdot II + II^2) $$After putting $ I = x^{5} $ and $ II = 1 $ , we have:
$$ x^{15}+1 = ( x^{5}+1 ) ( x^{10}-x^{5}+1 ) $$Step 2 :
To factor $ x^{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 = x $ and $ II = 1 $ , we have:
$$ x^{5}+1 = ( x+1 ) ( x^{4}-x^{3}+x^{2}-x+1 ) $$This page was created using
Polynomial Factoring Calculator