1. **State the problem:** We need to find which polynomial has a leading coefficient of 4 and a degree of 3. 2. **Recall definitions:** - The **degree** of a polynomial is the highest power of $x$ in the polynomial. - The **leading coefficient** is the coefficient of the term with the highest degree. 3. **Analyze each polynomial:** - Polynomial 1: $3x^4 - 2x^2 + 4x - 7$ - Degree is 4 (highest power is $x^4$) - Leading coefficient is 3 (coefficient of $x^4$) - Polynomial 2: $4 + x - 4x^2 + 5x^3$ - Degree is 3 (highest power is $x^3$) - Leading coefficient is 5 (coefficient of $x^3$) - Polynomial 3: $4x^4 - 3x^3 + 2x^2$ - Degree is 4 - Leading coefficient is 4 - Polynomial 4: $2x + x^2 + 4x^3$ - Degree is 3 - Leading coefficient is 4 4. **Conclusion:** The polynomial with degree 3 and leading coefficient 4 is polynomial 4: $2x + x^2 + 4x^3$. **Final answer:** Polynomial 4: $2x + x^2 + 4x^3$