The LCM of the polynomials $x y + y z + z x + y^{2} a n d x^{2} + x y + y z + z x$ is

x + y

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y + z

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(x + y) (y + z) (z + x)

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x^{2} + y^{2}

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Solution

The correct option is C $(x + y) (y + z) (z + x)$
$x y + y z + z x + y^{2} = x (y + z) + y (y + z)$
= $(y + z) (x + y)$
$x^{2} + x y + y z + z x = x (x + y) + z (y + x)$
= $(x + y) (x + z)$
$∴$ Reqd LCM $= (x + y) (y + z) (x + z)$

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