Unformatted text preview: g ( x ) = n X k =0 a k x 2 k is divisible by f ( x ). 5. Do there exist polynomials a ( x ) , b ( x ) , c ( y ) , d ( y ) with complex coeﬃcients such that 1 + xy + x 2 y 2 = a ( x ) c ( y ) + b ( x ) d ( y )? 6. Prove that for any polynomial p ( x ) of degree at least 2 with integer co-eﬃcients, there exists polynomial q ( x ) with integer coeﬃcients for which the polynomial p ( q ( x )) can be factored into a product of non-constant polynomials with integer coeﬃcients. 1...
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- Spring '08
- Polynomials, Prime number, Complex number