Determine if the expression \( 9 c^{5}+5 c^{3} \) is a polynomial or not. If it is a poly the type and degree of the polynomial.

Yes, the expression \( 9c^{5} + 5c^{3} \) is a **polynomial**. Here's a detailed breakdown: ### **1. Polynomial Verification** A **polynomial** is an algebraic expression composed of terms that are non-negative integer powers of a variable, combined using addition or subtraction. Each term consists of a coefficient multiplied by the variable raised to an exponent. For \( 9c^{5} + 5c^{3} \): - **Terms:** \( 9c^{5} \) and \( 5c^{3} \) - **Variable:** \( c \) - **Exponents:** 5 and 3 (both are non-negative integers) Since all conditions are satisfied, the expression is indeed a polynomial. ### **2. Type of Polynomial** The number of terms in a polynomial determines its type: - **Monomial:** 1 term - **Binomial:** 2 terms - **Trinomial:** 3 terms - **Polynomial:** More than 3 terms Given \( 9c^{5} + 5c^{3} \) has **2 terms**, it is classified as a **binomial**. ### **3. Degree of the Polynomial** The **degree** of a polynomial is the highest exponent of the variable in the expression. In \( 9c^{5} + 5c^{3} \): - The exponents are 5 and 3. - The highest exponent is **5**. Therefore, the degree of the polynomial is **5**. ### **Conclusion** - **Type:** Binomial - **Degree:** 5 **Final Statement:** \( 9c^{5} + 5c^{3} \) is a **binomial polynomial** of **degree five**.