Answer the questions about the following polynomial.
1, minus, 3, x, cubed
1−3x 
3
 
Answer
Attempt 1 out of 2

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 based on the components mentioned in the question.

1. **Polynomial type and number of terms**:  
   The polynomial \( 1 - 3x^3 \) has two terms: \( 1 \) (the constant term) and \( -3x^3 \) (the cubic term). Therefore, this is a binomial because it has exactly two terms.

2. **Constant term**:  
   The constant term in the polynomial is \( 1 \). This is the term that does not contain the variable \( x \).

3. **Leading term**:  
   The leading term of a polynomial is the term with the highest power of \( x \). In this polynomial, the term with the highest power of \( x \) is \( -3x^3 \). Therefore, 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 \( -3 \).

In summary:

- The polynomial is a **binomial** 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 polynomial change if the leading coefficient was positive?
3. What are the roots of the polynomial \( 1 - 3x^3 = 0 \)?
4. How would you graph the polynomial \( 1 - 3x^3 \)?
5. What happens to the polynomial if a linear term (e.g., \( 2x \)) is added?

**Tip:** The degree of a polynomial is determined by the highest power of the variable present in the expression.

Understand the polynomial 1 - 3x^3 with detailed analysis of its terms, constant term, leading term, and leading coefficient. This explanation covers basic polynomial concepts and is suitable for Grades 7-9 students.

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