The HCF of (2x^3 + 2x) ; (x^2 +1) ; (x^4 - 1)a) (x^2 + 1)b) (x - 1)c)

1.	The HCF of (2x^3 + 2x) ; (x^2 +1) ; (x^4 - 1)a) (x^2 + 1)b) (x - 1)c) 1d) (x + 1)
Answer» Answer: X8 – 1 = (X4)2 - 12 = (x4 + 1)(x4 - 1) = (x4 + 1)(x2 - 1) (x2 + 1) = (x4 + 1)(x2 + 1)(x + 1)(x - 1) [ ∴ a2 - b2 = (a + b)(a - b) ] x4 + 2X3 – 2x – 1 = (x4 - 1) + 2x3 – 2x = (x2 - 1) (x2 + 1) + 2x(x2 - 1) = (x2 + 1 + 2x)(x2 - 1) = (x + 1)2(x + 1)(x - 1) ∴ H.C.F = (x + 1) (x – 1) = (x2 - 1)

The HCF of (2x^3 + 2x) ; (x^2 +1) ; (x^4 - 1)a) (x^2 + 1)b) (x - 1)c) 1d) (x + 1)

Answer»

Answer:

X8 – 1 = (X4)2 - 12

= (x4 + 1)(x4 - 1)

= (x4 + 1)(x2 - 1) (x2 + 1)

= (x4 + 1)(x2 + 1)(x + 1)(x - 1)

[ ∴ a2 - b2 = (a + b)(a - b) ]

x4 + 2X3 – 2x – 1 = (x4 - 1) + 2x3 – 2x

= (x2 - 1) (x2 + 1) + 2x(x2 - 1)

= (x2 + 1 + 2x)(x2 - 1)

= (x + 1)2(x + 1)(x - 1)

∴ H.C.F = (x + 1) (x – 1) = (x2 - 1)

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The HCF of (2x^3 + 2x) ; (x^2 +1) ; (x^4 - 1)a) (x^2 + 1)b) (x - 1)c) 1d) (x + 1)​

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The HCF of (2x^3 + 2x) ; (x^2 +1) ; (x^4 - 1)a) (x^2 + 1)b) (x - 1)c) 1d) (x + 1)