Find the G.C.D. of the polynomials (x-2)^{2}( | vedclass

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(C) Let the two polynomials be $p(x) = (x-2)^{2}(x+3)(x-4)$ and $q(x) = (x-2)(x+2)(x-5)$.To find the $G.C.D.$ (Greatest Common Divisor),we identify th

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$(x-2)$

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(C) Let the two polynomials be $p(x) = (x-2)^{2}(x+3)(x-4)$ and $q(x) = (x-2)(x+2)(x-5)$.To find the $G.C.D.$ (Greatest Common Divisor),we identify the common factors present in both expressions.The factors of $p(x)$ are $(x-2)$,$(x-2)$,$(x+3)$,and $(x-4)$.The factors of $q(x)$ are $(x-2)$,$(x+2)$,and $(x-5)$.The only common factor present in both polynomials is $(x-2)$.Therefore,the $G.C.D.$ of the given polynomials is $(x-2)$.

Find the $G.C.D.$ of the polynomials $(x-2)^{2}(x+3)(x-4)$ and $(x-2)(x+2)(x-5)$.

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