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  4. Which of the following is a factor of x3+3 n x2-3 m n x-m3 ? (where p and q are constants)

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Q. Which of the following is a factor of $x^3+3 n x^2-3 m n x-m^3$ ? (where $p$ and $q$ are constants)

Remainder and Factor Theorems

Solution:

Let, $f(x)=x^3+3 m x^2-3 m n x-n^3$
From the options,
$f(m)=m^3+3 n m^2-3 n m^2-m^3$
Hence, $x-m$ is a factor of $f(x)$.