Find the G.C.D. of 3+13 x-30 x^{2} and 25 x^{ | vedclass

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(B) Let $p(x) = 3 + 13x - 30x^2$.Rearranging the terms: $p(x) = -30x^2 + 13x + 3$.Factorizing $p(x) = -30x^2 + 18x - 5x + 3 = -6x(5x - 3) - 1(5x - 3)

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$5 x-3$

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(B) Let $p(x) = 3 + 13x - 30x^2$.Rearranging the terms: $p(x) = -30x^2 + 13x + 3$.Factorizing $p(x) = -30x^2 + 18x - 5x + 3 = -6x(5x - 3) - 1(5x - 3) = -(6x + 1)(5x - 3)$.Let $q(x) = 25x^2 - 30x + 9$.This is a perfect square trinomial: $q(x) = (5x)^2 - 2(5x)(3) + 3^2 = (5x - 3)^2$.The $G.C.D.$ (Greatest Common Divisor) is the highest common factor between $p(x)$ and $q(x)$.Comparing $p(x) = -(6x + 1)(5x - 3)$ and $q(x) = (5x - 3)(5x - 3)$,the common factor is $(5x - 3)$.Therefore,the $G.C.D.$ is $(5x - 3)$.

Find the $G.C.D.$ of $3+13 x-30 x^{2}$ and $25 x^{2}-30 x+9$.

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