Find the L.C.M. of the polynomials (x+3)(-6x^ | vedclass

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(A) Let $p(x) = (x+3)(-6x^2+5x+4)$.Factorizing the quadratic expression: $-6x^2+5x+4 = -6x^2+8x-3x+4 = -2x(3x-4)-1(3x-4) = -(3x-4)(2x+1)$.So,$p(x) = -

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$-(x+3)^2(3x-4)(2x+1)$

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(A) Let $p(x) = (x+3)(-6x^2+5x+4)$.Factorizing the quadratic expression: $-6x^2+5x+4 = -6x^2+8x-3x+4 = -2x(3x-4)-1(3x-4) = -(3x-4)(2x+1)$.So,$p(x) = -(x+3)(3x-4)(2x+1)$.Let $q(x) = (2x^2+7x+3)(x+3)$.Factorizing the quadratic expression: $2x^2+7x+3 = 2x^2+6x+x+3 = 2x(x+3)+1(x+3) = (2x+1)(x+3)$.So,$q(x) = (2x+1)(x+3)(x+3) = (x+3)^2(2x+1)$.The $L.C.M.$ is the product of the highest powers of all prime factors present in the expressions.$L.C.M. = -(x+3)^2(3x-4)(2x+1)$.

Find the $L.C.M.$ of the polynomials $(x+3)(-6x^2+5x+4)$ and $(2x^2+7x+3)(x+3)$.

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