Find the G.C.D. of 8(x^{4}-16) and 12(x^{3}-8 | vedclass

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(B) Let $p(x) = 8(x^{4}-16)$.Factorizing $p(x)$:$p(x) = 8(x^{2}-4)(x^{2}+4) = 8(x-2)(x+2)(x^{2}+4) = 4 	imes 2(x-2)(x+2)(x^{2}+4)$.Let $q(x) = 12(x^{

Vedclass · Accepted Answer

$4(x-2)$

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(B) Let $p(x) = 8(x^{4}-16)$.Factorizing $p(x)$:$p(x) = 8(x^{2}-4)(x^{2}+4) = 8(x-2)(x+2)(x^{2}+4) = 4 	imes 2(x-2)(x+2)(x^{2}+4)$.Let $q(x) = 12(x^{3}-8)$.Factorizing $q(x)$ using the formula $a^{3}-b^{3} = (a-b)(a^{2}+ab+b^{2})$:$q(x) = 12(x-2)(x^{2}+2x+4) = 4 	imes 3(x-2)(x^{2}+2x+4)$.The $G.C.D.$ is the product of the common factors with the lowest power.The common factor is $4(x-2)$.Therefore,the $G.C.D.$ is $4(x-2)$.

Find the $G.C.D.$ of $8(x^{4}-16)$ and $12(x^{3}-8)$.

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