F4 Maths Factor Theorem 5

2x^4 - x^3 - 6x^2 - x + 2 = 0
Divided both sides by x^2
2x^2 - x - 6 - 1/x + 2/x^2 = 0
(2x^2 + 4 + 2/x^2) - (x + 1/x) - 10 = 0
2(x + 1/x)^2 - (x + 1/x) - 10 = 0
Let t = x + 1/x
2t^2 - t - 10 = 0
(t + 2)(2t - 5) = 0
t = -2 or t = 5/2
when t = -2
x + 1/x = -2
x^2 + 2x + 1 = 0
(x + 1)^2 = 0
x = -1
when t = 5/2
x + 1/x = 5/2
2x^2 - 5x + 2 = 0
(2x - 1)(x - 2) = 0
x = 2 or x = 1/2
Therefore the roots are -1, 1/2 and 2