jmc

We see that the largest common factor of the coefficients is $2$ and that $x^1$ is the largest power of $x$ which divides all the terms, so we can factor out $2x$ from each term. Doing so gives: $$\begin{array}{rl}30x^3-8x^2+20x& =2x\cdot 15x^2+2x\cdot (-4x)+2x\cdot 10\\ & =\boxed{2x(15x^2-4x+10)}\end{array}$$