Math Problem Statement

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 .

Solution

The given polynomial is 13x31 - 3x^3. Let's analyze it based on the components mentioned in the question.

  1. Polynomial type and number of terms:
    The polynomial 13x31 - 3x^3 has two terms: 11 (the constant term) and 3x3-3x^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 11. This is the term that does not contain the variable xx.

  3. Leading term:
    The leading term of a polynomial is the term with the highest power of xx. In this polynomial, the term with the highest power of xx is 3x3-3x^3. Therefore, 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.

In summary:

  • The polynomial is a binomial 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 polynomial change if the leading coefficient was positive?
  3. What are the roots of the polynomial 13x3=01 - 3x^3 = 0?
  4. How would you graph the polynomial 13x31 - 3x^3?
  5. What happens to the polynomial if a linear term (e.g., 2x2x) is added?

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