Questions: Give the name (monomial, binomial, trinomial, etc.) and the degree of the polynomial. 2x^3 + 3x^2 + 6x Name = [?] Degree =

Give the name (monomial, binomial, trinomial, etc.) and the degree of the polynomial. 2x^3 + 3x^2 + 6x Name = [?] Degree =
Transcript text: /3/work/leaSnrmT-bDDxEgsmpNncQQ Unit Exam - Polynomials Give the name (monomial, oinomial, trinomial, etc.) and the degree of the polynomial. \[ \begin{array}{c} 2 x^{3}+3 x^{2}+6 x \\ \text { Name }=[?] \\ \text { Degree }= \end{array} \]
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Solution

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Solution Steps

To determine the name and degree of the polynomial, we need to count the number of terms and identify the highest power of the variable. A polynomial with one term is a monomial, two terms is a binomial, three terms is a trinomial, and more than three terms is simply called a polynomial. The degree of the polynomial is the highest exponent of the variable.

Step 1: Identify the Type of Polynomial

A polynomial is classified based on the number of terms it contains:

  • A monomial has one term.
  • A binomial has two terms.
  • A trinomial has three terms.
  • A polynomial with more than three terms is simply called a polynomial.

The given polynomial is:

\[ 2x^3 + 3x^2 + 6x \]

This polynomial has three terms: \(2x^3\), \(3x^2\), and \(6x\). Therefore, it is a trinomial.

Step 2: Determine the Degree of the Polynomial

The degree of a polynomial is the highest power of the variable \(x\) in the polynomial. In the given polynomial:

\[ 2x^3 + 3x^2 + 6x \]

The degrees of the terms are:

  • \(2x^3\) has a degree of 3.
  • \(3x^2\) has a degree of 2.
  • \(6x\) has a degree of 1.

The highest degree among these is 3. Therefore, the degree of the polynomial is 3.

Final Answer

  • Name: Trinomial
  • Degree: 3

\[ \boxed{\text{Name: Trinomial, Degree: 3}} \]

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