Pregunta
Select the correct choice below and fill in the answer box to complete your choice. B. The polynomial cannot be simplified. The polynomial written in descending powers is \( 7 x^{3}-3 x \). The degree is 3 . (Type a whole number.) Which term describes the simplified polynomial? Monomial Trinomial Binomial None of these
Ask by Howell Williams. in the United Arab Emirates
Mar 14,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The polynomial \( 7x^3 - 3x \) is a **binomial**.
Solución
To determine the correct term that describes the polynomial \( 7x^3 - 3x \), we need to analyze the number of terms in the polynomial.
1. **Identify the terms**: The polynomial \( 7x^3 - 3x \) consists of two terms:
- \( 7x^3 \)
- \( -3x \)
2. **Count the terms**:
- Since there are two terms, we classify the polynomial based on the number of terms:
- A **monomial** has 1 term.
- A **binomial** has 2 terms.
- A **trinomial** has 3 terms.
Since \( 7x^3 - 3x \) has 2 terms, it is classified as a **binomial**.
Thus, the correct choice is:
**Binomial**.
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The Deep Dive
The simplified polynomial \( 7x^3 - 3x \) has two distinct terms that are not like terms. Therefore, it fits the category of a binomial, as it is composed of two terms. A quick reminder about polynomials: they can consist of one term (monomial), two terms (binomial), three terms (trinomial), or more. In this case, you’ve got one term with \( x^3 \) and another with \( x \), making it a binomial!

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