1.

Find the HCF of x3 + x2 + x + 1 and x4 – 1.

Answer»

x3 + x2 + x + 1 = x2(x + 1) + 1 (x + 1)

= (x + 1) (x2 + 1)

x4 - 1 = (x2)2 – 1

= (x2 + 1) (x2 – 1)

= (x2 + 1) (x + 1) (x – 1)

H.C.F. = (x2 + 1)(x + 1)



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