1.

HCF of \(x^3 - 1\) and \(x^4 + x^2 + 1\) will be(a) (x – 1) (b) x2 + x + 1(c) x2 - x + 1 (d) x2 - x - 1

Answer»

(b) x2 + x + 1

\(x^3 - 1 = (x - 1)(x^2 + x +1)\)

\(x^4 + x^2 + 1 = x^4 + 2x^2 + 1 - x^2 = (x^2 + 1) - x^2\) 

= \((x^2+1-x)(x^2+1+x)\)

∴ Reqd. HCF = x2 + x + 1


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