Find the G.C.D. of (x+4)^{2}(x-3)^{2} and (x- | vedclass

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(C) Let the two polynomials be $p(x) = (x+4)^{2}(x-3)^{2}$ and $q(x) = (x-1)(x+4)(x-3)^{2}$.The $G.C.D.$ (Greatest Common Divisor) is the product of t

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$(x+4)(x-3)^{2}$

Vedclass · Answer

(C) Let the two polynomials be $p(x) = (x+4)^{2}(x-3)^{2}$ and $q(x) = (x-1)(x+4)(x-3)^{2}$.The $G.C.D.$ (Greatest Common Divisor) is the product of the lowest powers of all common factors present in the given polynomials.Factors of $p(x)$ are $(x+4)^{2}$ and $(x-3)^{2}$.Factors of $q(x)$ are $(x-1)$,$(x+4)$,and $(x-3)^{2}$.The common factors are $(x+4)$ and $(x-3)^{2}$.The lowest power of $(x+4)$ is $(x+4)^{1}$.The lowest power of $(x-3)$ is $(x-3)^{2}$.Therefore,the $G.C.D.$ is $(x+4)(x-3)^{2}$.

Find the $G.C.D.$ of $(x+4)^{2}(x-3)^{2}$ and $(x-1)(x+4)(x-3)^{2}$.

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