>>578
m≠0 のとき
　(mx)^2 + 16mx +m(m+2)= (mx+8)^2 + (m+1)^2 -65,

　m+1 = ±1, ±4, ±7, ±8、
　m = -9, -8, -5, -2, 3, 6, 7

m=-9, f(x) = -9x^2 +16x -7 = -(x-1)(9x-7), (1, 7/9)　
m=-8, f(x) = -8x^2 +16x -6 = -2(2x-1)(2x-3), 不可
m=-5, f(x) = -5x^2 +16x -3 = -(x-3)(5x-1), (3, 1/5)　
m=-2, f(x) = -2x^2 +16x = -2x(x-8), (0, 8)　
m= 3, f(x) = 3x^2 +16x +5 = (x-5)(3x-1), (-5, -1/3)　
m= 6, f(x) = 6x^2 +16x +8 = 2(x+2)(3x+2), (-2, -2/3)　
m= 7, f(x) = 7x^2 +16x +9 = (x+1)(7x+9), (-1, -9/7)