Math Problem Statement

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 .

Solution

The given polynomial is 13x31 - 3x^3. Let's analyze it step by step to answer the questions:

  1. Number of Terms:
    The polynomial 13x31 - 3x^3 consists of two terms: 11 (the constant term) and 3x3-3x^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 xx. In this polynomial, the constant term is 11.

  3. Leading Term:
    The leading term of a polynomial is the term with the highest power of xx. Here, the term with the highest power of xx is 3x3-3x^3. Thus, the leading term is 3x3-3x^3.

  4. Leading Coefficient:
    The leading coefficient is the coefficient of the leading term. For the term 3x3-3x^3, the coefficient is 3-3. Hence, the leading coefficient is 3-3.

To summarize:

  • The polynomial represents a polynomial with 2 terms.
  • The constant term is 1.
  • The leading term is 3x3-3x^3.
  • The leading coefficient is 3-3.

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 13x31 - 3x^3?
  2. How would the behavior of the polynomial change if the leading coefficient was positive?
  3. Can the polynomial 13x31 - 3x^3 be factored further?
  4. What are the roots of the polynomial equation 13x3=01 - 3x^3 = 0?
  5. How would the graph of 13x31 - 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.