The expression $x^{2} - y^{2} - z^{2} - 2 y z + x + y + z$ has a factor

x - y + z + 1

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- x + y + z

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x + y - z + 1

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x - y - z + 1

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Solution

The correct option is A $x - y - z + 1$
We have,
$= x^{2} - y^{2} - z^{2} - 2 y z + x + y + z$
$= x^{2} - {(y + z)}^{2} + (x + y + z)$
$= (x - y - z) (x + y + z) + (x + y + z)$
$= (x + y + z) (x - y - z + 1)$

Hence, this is the answer.

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