1. **State the problem:** Factor out the greatest common factor (GCF) from the polynomial $$26y^5 + 39y^3$$. 2. **Identify the GCF:** - For the coefficients 26 and 39, the GCF is 13 because 13 divides both 26 and 39. - For the variable parts $$y^5$$ and $$y^3$$, the GCF is the lowest power of $$y$$, which is $$y^3$$. 3. **Write the GCF:** $$13y^3$$. 4. **Factor out the GCF:** $$26y^5 + 39y^3 = 13y^3(\frac{26y^5}{13y^3} + \frac{39y^3}{13y^3})$$ 5. **Simplify inside the parentheses:** $$= 13y^3(\cancel{13} \times 2 y^{5-3} / \cancel{13} + \cancel{13} \times 3 y^{3-3} / \cancel{13})$$ $$= 13y^3(2y^2 + 3)$$ 6. **Final factored form:** $$\boxed{13y^3(2y^2 + 3)}$$