What are the values of c when the HCF of x 3 + c x 2 - x + 2c and x 2 + cx - 2 over the rational is a linear polynomial?

Find HCF of x³ +c x² -x + 2c and x² + cx - 2 by long division method and get remainder
∴ Remainder = 2c - 2/c
Since,remainder should be zero
∴ 2c² - 2 = 0
⇒ 2(c² -1) = 0 ⇒ c= ± 1