Chọn a=−1+√80412⇒a2=a+2010Chọn P(x)=(x−a)2010Ta có:P(x2−2010)=(x2−a−2010)2010 =(x2−a2)2010 =(x−a)2010(x+a)2010=P(x)(x+a)2010Suy ra: P(x2−2010)⋮P(x), thỏa mãn.
Ch
oose a=−1+√80412⇒a2=a+2010Ch
oose P(x)=(x−a)2010We have:
P(x2−2010)=(x2−a−2010)2010 =(x2−a2)2010 =(x−a)2010(x+a)2010=P(x)(x+a)2010It follows tha
t P(x2−2010)⋮P(x),
sat
isfied.