Answer the questions about the following polynomial.
1, minus, 3, x, cubed
1−3x
3

The expression represents a
polynomial with
terms. The constant term is
, the leading term is
, and the leading coefficient is
.

The given polynomial is \( 1 - 3x^3 \). Let's analyze it step by step to answer the questions:

1. **Number of Terms**:  
   The polynomial \( 1 - 3x^3 \) consists of two terms: \( 1 \) (the constant term) and \( -3x^3 \) (the cubic term). Therefore, this is a polynomial with **2 terms**.

2. **Constant Term**:  
   The constant term is the term that does not contain the variable \( x \). In this polynomial, the constant term is \( 1 \).

3. **Leading Term**:  
   The leading term of a polynomial is the term with the highest power of \( x \). Here, the term with the highest power of \( x \) is \( -3x^3 \). Thus, the leading term is \( -3x^3 \).

4. **Leading Coefficient**:  
   The leading coefficient is the coefficient of the leading term. For the term \( -3x^3 \), the coefficient is \( -3 \). Hence, the leading coefficient is \( -3 \).

To summarize:

- The polynomial represents a polynomial with **2 terms**.
- The constant term is **1**.
- The leading term is **\(-3x^3\)**.
- The leading coefficient is **\(-3\)**.

Would you like more details or have any questions?

Here are some related questions for further exploration:

1. What is the degree of the polynomial \( 1 - 3x^3 \)?
2. How would the behavior of the polynomial change if the leading coefficient was positive?
3. Can the polynomial \( 1 - 3x^3 \) be factored further?
4. What are the roots of the polynomial equation \( 1 - 3x^3 = 0 \)?
5. How would the graph of \( 1 - 3x^3 \) look, and where would it intersect the y-axis?

**Tip:** Remember, the leading term and leading coefficient play a crucial role in determining the end behavior of the polynomial's graph.

Explore the polynomial 1 - 3x^3 and understand its structure, including the number of terms, constant term, leading term, and leading coefficient. This detailed analysis covers key concepts in polynomials and is suitable for students in Grades 7-9.

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