Find the L.C.M. of the polynomials: 16-4x^{2} | vedclass

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(A) Given polynomials are $p(x) = 16 - 4x^{2}$ and $q(x) = x^{2} + x - 6$.Step $1$: Factorize $p(x)$.$p(x) = 16 - 4x^{2} = 4(4 - x^{2}) = 4(2 - x)(2 +

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

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(A) Given polynomials are $p(x) = 16 - 4x^{2}$ and $q(x) = x^{2} + x - 6$.Step $1$: Factorize $p(x)$.$p(x) = 16 - 4x^{2} = 4(4 - x^{2}) = 4(2 - x)(2 + x) = -4(x - 2)(x + 2)$.Step $2$: Factorize $q(x)$.$q(x) = x^{2} + x - 6 = x^{2} + 3x - 2x - 6 = x(x + 3) - 2(x + 3) = (x + 3)(x - 2)$.Step $3$: Find the $L.C.M.$The $L.C.M.$ is the product of the highest powers of all prime factors present in the expressions.$L.C.M. = -4(x - 2)(x + 2)(x + 3)$.Simplifying the expression:$L.C.M. = -4(x^{2} - 4)(x + 3)$.

Find the $L.C.M.$ of the polynomials: $16-4x^{2}$ and $x^{2}+x-6$.

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