Question

If $x-a$ is a factor of $x^3-3x^{2}a+2a^{2}x+b$, then the value of $b$ is

Answer 1

Given: $x^3-3x^{2}a+2a^{2}x+b$

Let, $f\left(x\right)=x^3-3x^{2}a+2a^{2}x+b$

$\because x-a$ is a factor of $f\left(x\right)$, by factor theorem $f\left(a\right)=0$

$\Rightarrow (a{)}^3-3\times (a{)}^2\times a+2\times (a{)}^2\times a+b=0$

$\Rightarrow a^3-3a^3+2a^3+b=0$

$\because$ The value of $bis0$.

Hence, option (A) is the correct answer.