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