Question

How do you find all the roots of the equation: x^5 + 3x^4 + 8x^3 + 24x^2 - 9x - 27 = 0?

Answer 1

x^5 + 3x^4 + 8x^3 + 24x^2 - 9x - 27
= x^5 -- x^4 + 4x^4 -- 4x^3 + 12x^3 -- 12x^2 + 36x^2 + 27x -- 27
= (x -- 1)(x^4 + 4x^3 + 12x^2 + 36x + 27)
= (x -- 1)(x + 1)(x^3 + 3x^2 + 9x + 27)
= (x -- 1)(x + 1)(x + 3)(x^2 + 9)