1. **Problem statement:** Factor out the greatest common factor (GCF) from the term $2x^4 - x^3$. 2. **Identify the GCF:** - Look at the coefficients: 2 and 1 (implicit in $-x^3$). - Look at the variable parts: $x^4$ and $x^3$. - The GCF of the coefficients is 1. - The GCF of the variables is the lowest power of $x$, which is $x^3$. 3. **Divide each term by the GCF:** $$\frac{2x^4}{x^3} = 2x$$ $$\frac{-x^3}{x^3} = -1$$ 4. **Write the factored form:** $$x^3 \cdot (2x - 1)$$ 5. **Explanation:** Factoring means expressing the original expression as a product of the GCF and the simplified expression inside parentheses. Here, $x^3$ is the largest power of $x$ common to both terms, so we factor it out. **Final answer:** $$2x^4 - x^3 = x^3 (2x - 1)$$