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Find the GCD of the following by division algorithm 2x^4 + 13.x^3 + 21 x^2 + 23x + 7, x^3 + 3x^2 + 3x + 1, x^2 + 2x + 1.

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Find the GCD of the following by division algorithm 2x4 + 13.x3 + 21 x2 + 23x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1.

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2x4 + 13x3 + 27x2 + 23x + 7,

x3 + 3x2 + 3x + 1, x2 + 2x + 1.

By division algorithm, first divide

∴ (x + 1)2 is G.C.D of x3 + 3x2 + 3x + 1 and x2 + 2x + 1.

Next let us divide

2x4 + 13x3 + 27x2 + 23x + 7 by x2 + 2x + 1

∴ G.C.D of 2x4 + 13x3 + 21x2 + 23x + 7, x3 + 3x2 + 3x + 1, x2 + 2x + 1 is (x + 1)2.

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