Answer
$9x(2x^2-7x+1)$
Work Step by Step
$18x^3-63x^2+9x$
$9x(2x^2-7x+1)$
The only pairs of numbers whose product is 2 (the coefficient of $x^2$) are $1$ and $2$ or $-1$ and $-2$.
The only pairs of numbers whose product is 1 (the value for $c$) are $1$ and $1$ or $-1$ and $-1$.
There is no combination of the pairs of numbers to get a value of $-7$, so we are at the factored form of the polynomial.