Question

Which of the following is a factor of $a^2{x}^3-2ab{x}^2+b^{2}x$?

Answer 1

$a^2{x}^3-2ab{x}^2+b^{2}x=x(a^2{x}^2-2abx+b^2)=x\left(\right(ax{)}^2-2\left(ax\right)b+b^2)=x(ax-b{)}^2=x(ax-b)(ax-b)$

$ax-b$ is a factor of $a^2{x}^3-2ab{x}^2+b^{2}x.$