Find the G.C.D. of the polynomials 6 x^{2}+11 | vedclass

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(C) Let the first polynomial be $p(x) = 6 x^{2} + 11 x + 3$.By splitting the middle term: $6 x^{2} + 9 x + 2 x + 3 = 3 x(2 x + 3) + 1(2 x + 3) = (2 x

Vedclass · Accepted Answer

$2 x+3$

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(C) Let the first polynomial be $p(x) = 6 x^{2} + 11 x + 3$.By splitting the middle term: $6 x^{2} + 9 x + 2 x + 3 = 3 x(2 x + 3) + 1(2 x + 3) = (2 x + 3)(3 x + 1)$.Let the second polynomial be $q(x) = 2 x^{2} + x - 3$.By splitting the middle term: $2 x^{2} + 3 x - 2 x - 3 = x(2 x + 3) - 1(2 x + 3) = (2 x + 3)(x - 1)$.The $G.C.D.$ is the common factor between the two polynomials.Therefore,$G.C.D. = (2 x + 3)$.

Find the $G.C.D.$ of the polynomials $6 x^{2}+11 x+3$ and $2 x^{2}+x-3$.

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