By Rational Root Theorem, all rational roots of a polynomial are in the form $\frac{p}{q}$, where $p$ divides the constant term $-3$ and $q$ divides the leading coefficient $-2$. One such root is $-1$. Factor the polynomial by dividing it by $x+1$. Polynomial $-2x^{8}+2x^{7}-2x^{6}+2x^{5}+4x-3$ is not factored since it does not have any rational roots.
