What are the values of c when the HCF of x3 + c x2 -

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What are the values of c when the HCF of x³ + c x² - x + 2c and x² + cx - 2 over the rational is a linear polynomial ?

1. +1
2. +2
3. +1
4. +4

Correct Option: A

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