1. **State the problem:** We need to find the sum of the polynomials $(5x^3 - 2x^2 + x - 3) + (-2x^2 + x + 5x + 1)$. 2. **Recall the rule for adding polynomials:** Combine like terms, which are terms with the same variable raised to the same power. 3. **Group like terms:** $$ (5x^3) + (-2x^2 - 2x^2) + (x + x + 5x) + (-3 + 1) $$ 4. **Simplify each group:** - For $x^3$: $5x^3$ - For $x^2$: $-2x^2 - 2x^2 = -4x^2$ - For $x$: $x + x + 5x = 7x$ - Constants: $-3 + 1 = -2$ 5. **Write the final simplified polynomial:** $$ 5x^3 - 4x^2 + 7x - 2 $$ This is the sum of the given polynomials.