Gcf Polynomial 9Daf01

1. **State the problem:** Find the greatest common factor (GCF) of the polynomial expression $$3x + 5xy - 2x^5$$. 2. **Identify the terms:** The terms are $$3x$$, $$5xy$$, and $$-2x^5$$. 3. **Find the GCF of the coefficients:** The coefficients are $$3$$, $$5$$, and $$-2$$. The GCF of $$3$$, $$5$$, and $$2$$ is $$1$$ (since 3, 5, and 2 have no common factors other than 1). 4. **Find the GCF of the variables:** - The first term has $$x^1$$. - The second term has $$x^1 y^1$$. - The third term has $$x^5$$. The common variable factor is $$x$$ raised to the smallest power among the terms, which is $$x^1$$. 5. **Combine the GCF:** The GCF is $$1 \times x = x$$. 6. **Final answer:** The greatest common factor of $$3x + 5xy - 2x^5$$ is $$\boxed{x}$$.