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Integer coefficients (Posted on 2007-03-13) Difficulty: 2 of 5
Determine if it is possible that p(x)*q(x)= x5+9x+1, if p(x) and q(x) must be polynomials of degree 1 or higher, with integer coefficients.

See The Solution Submitted by K Sengupta    
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No Linear Factors Comment 3 of 3 |
Determining whether there are linear factors (degree 1 polynomial)  is easy.  From the coefficient of the lead term and the constant (1 and 1), we can conclude the only possible rational roots are 1 and -1.  Since neither 1 or -1 is a root, there are no linear factors.
  Posted by Brian Smith on 2007-03-14 21:09:54
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