1.

Find the HCF of X4 – 1 and X4 + 5X2 + 4.1). (X2 + 1)2). (X + 1)3). (X2 – 1)4). 1

Answer»

X4 – 1 = (X2)2 – (1)2

⇒ (X2 – 1) (X2 + 1)

⇒ (X2 – 12) (X2 + 1)

⇒ (X – 1) (X + 1) (X2 + 1)...(1)

 X4 + 5X2 + 4

⇒ X4 + X2 + 4X2 + 4

⇒ X2 (X2 + 1) + 4(X2 + 1)

⇒ (X2 + 1) (X2 + 4)...(2)

Common factor from both the EQ. (1) and (2)

∴ HCF = (X2 + 1)


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