(a) Consider the sum of squares x2 + 9. If the sum can be factored, then there are integers m and n such that x2 + 9 = (x + m)(x + n). Write two equations relating the sum and the product of m and n to the coefficients in x2 + 9.
(b) Show that there are no integers m and n that satisfy both equations you wrote in part (a). What can you conclude?