Learn how to solve problems step by step online. Simplify the expression (w^2+2w+-80)/(2w^3-24w^264w). We can factor the polynomial 2w^3-24w^2+64w using the rational root theorem, which guarantees that for a polynomial of the form a_nx^n+a_{n-1}x^{n-1}+\dots+a_0 there is a rational root of the form \pm\frac{p}{q}, where p belongs to the divisors of the constant term a_0, and q belongs to the divisors of the leading coefficient a_n. List all divisors p of the constant term a_0, which equals 0. Next, list all divisors of the leading coefficient a_n, which equals 2. The possible roots \pm\frac{p}{q} of the polynomial 2w^3-24w^2+64w will then be. We can factor the polynomial 2w^3-24w^2+64w using synthetic division (Ruffini's rule). We found that 4 is a root of the polynomial.

Simplify the expression (w^2+2w+-80)/(2w^3-24w^264w)