Question
Factor polynomial $$ v^{4}-16 $$
Answer
$$ v^{4}-16 = ( v-2 )( v+2 )( v^{2}+4 ) $$
Explanation
Step 1 :
Rewrite $ v^{4}-16 $ as:
$$ v^{4}-16 = (v^{2})^2 - (4)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = v^{2} $ and $ II = 4 $ , we have:
$$ v^{4}-16 = (v^{2})^2 - (4)^2 = ( v^{2}-4 ) ( v^{2}+4 ) $$Step 2 :
Rewrite $ v^{2}-4 $ as:
$$ v^{2}-4 = (v)^2 - (2)^2 $$Now we can apply the difference of squares formula.
$$ I^2 - II^2 = (I - II)(I + II) $$After putting $ I = v $ and $ II = 2 $ , we have:
$$ v^{2}-4 = (v)^2 - (2)^2 = ( v-2 ) ( v+2 ) $$This page was created using
Polynomial Factoring Calculator