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.

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