Question

Which of the following is a factor of $3x^3-2x^{2}y-13x{y}^2+10y^3$

• A. $x+y$
• B. $x-2y$
• C. $x+2y$
• D. $x-y$

Answer 1

The correct option is B $x-2y$

Let, $p\left(x\right)=3x^3-2x^{2}y-13x{y}^2+10y^3$
put $x=2y$ in $p\left(x\right)$
$p\left(2y\right)=3{\left(2y\right)}^3-2{\left(2y\right)}^{2}y-13\left(2y\right){\left(y\right)}^2+10{\left(y\right)}^3$
$=24y^3-8y^3-26y^3+10y^3$
$=34y^3-34y^3=0$
Since, $p\left(2y\right)=0$
$\therefore x-2y$ is a factor of $p\left(x\right)$
Option B is correct.