A Polynomial which Factors, but has no Roots: Give an example of a polynomial f(x) with...

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A Polynomial which Factors, but has no Roots: Give an example of a polynomial f(x) with integer coefficients which factors (poly mod n), (i.e. is the product of polynomials of smaller degree poly mod n) but which has no roots, i.e., for which there are no integers x such that f(x) = 0 (mod n). Remark: Your solution should give a specific integer n, and give all of the coefficients of f(x). It should show that f(r) really does factor, and it should prove that f(r) has no roots. It might help to first find some polynomials that have no roots. A Polynomial which Factors, but has no Roots: Give an example of a polynomial f(x) with integer coefficients which factors (poly mod n), (i.e. is the product of polynomials of smaller degree poly mod n) but which has no roots, i.e., for which there are no integers x such that f(x) = 0 (mod n). Remark: Your solution should give a specific integer n, and give all of the coefficients of f(x). It should show that f(r) really does factor, and it should prove that f(r) has no roots. It might help to first find some polynomials that have no roots. A Polynomial which Factors, but has no Roots: Give an example of a polynomial f(x) with integer coefficients which factors (poly mod n), (i.e. is the product of polynomials of smaller degree poly mod n) but which has no roots, i.e., for which there are no integers x such that f(x) = 0 (mod n). Remark: Your solution should give a specific integer n, and give all of the coefficients of f(x). It should show that f(r) really does factor, and it should prove that f(r) has no roots. It might help to first find some polynomials that have no roots.

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Sure I can help with this The prompt asks for a polynomial with integer co... View the full answer