Question
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Determine whether the given polynomial is a monomial, binomial, trinomial or, other polynomial. Then indicate the degree of the polynomial. 1) \( 3 h^{3}+2 h^{2}-11 \) The type of the given polynomial is: A Monomial B Binomial C Trinomial D Polynomial Its degree is: Enter your answer (a) -1 (?) The type of the given polynomial is: A Monomial B Binomial (E) Trinomial

Ask by Cervantes Adkins. in the United States
Mar 11,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The polynomial is a trinomial with a degree of 3.

Solution

The polynomial is \[ 3h^3 + 2h^2 - 11. \] **Step 1: Classify the Polynomial** A polynomial is classified by the number of terms: - A monomial has 1 term. - A binomial has 2 terms. - A trinomial has 3 terms. Since this polynomial has 3 terms, it is a **trinomial**. **Step 2: Determine the Degree** The degree of a polynomial is the highest exponent of the variable in the expression. Here: - The term \(3h^3\) has exponent 3. - The term \(2h^2\) has exponent 2. - The constant \(-11\) can be considered as \(h^0\), with exponent 0. The highest exponent is \(3\). Hence, the degree of the polynomial is \(3\). **Answer:** - The type of the given polynomial is: **Trinomial** - Its degree is: \(3\)

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This polynomial, \( 3h^{3} + 2h^{2} - 11 \), is classified as a trinomial because it contains three terms. The terms are \( 3h^{3} \), \( 2h^{2} \), and \(-11\). As for the degree of the polynomial, we look for the highest exponent of the variable \( h \), which here is 3 (from \( 3h^{3} \)). Therefore, the degree of this polynomial is 3. So your answers would be: The type of the given polynomial is: **C Trinomial** Its degree is: **3**

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