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Relationship between LCM and GCD

The LCM of po...

Question

The LCM of polynomials $x^{3} + 3 x^{2} + 3 x + 1, x^{2} + 2 x + 1 a n d x^{2} - 1$ is

(x^{2} - 1) {(x + 1)}^{2}

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(x^{2} + 1) {(x - 1)}^{2}

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(x^{2} - 1) {(x - 1)}^{2}

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{(x + 1)}^{3}

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Solution

The correct option is A $(x^{2} - 1) {(x + 1)}^{2}$
$x^{3} + 3 x^{2} + 3 x + 1 = {(x + 1)}^{3}$
$x^{2} + 2 x + 1 = {(x + 1)}^{2}$
$x^{2} - 1 = (x + 1) (x - 1)$
$∴$ Reqd LCM = $(x - 1) {(x + 1)}^{3}$
= $(x^{2} - 1) {(x + 1)}^{2}$

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