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