If x³ + 3px + q is a factor of expression (x² + k²) then show that 4p³ + q² = 0
a cubic cannot be a factor of a quadratic.
However, if (x^2+k^2) is a factor of (x^3 + 3px + q) then
x^3 + 3px + q = (x^2 + k^2)(x+m) = x^3 + mx^2 + k^2 x + k^2 m
equating coefficients, we get
m=0
so q=0 and 3p = k^2
but if q=0 then that means 4p^3 = 0
I suspect something has been garbled here.