Math Problem Statement

What is this equations leading term?

Solution

The expression in the image is:

3xx58+1x33x - \frac{x^5}{8} + 1 - x^3

To determine the leading term, we need to identify the term with the highest power of xx.

The terms in the expression are:

  • 3x3x (degree 1)
  • x58-\frac{x^5}{8} (degree 5)
  • 11 (degree 0, a constant term)
  • x3-x^3 (degree 3)

The term with the highest power of xx is x58-\frac{x^5}{8}.

Therefore, the leading term is:

x58-\frac{x^5}{8}

Would you like more details or have any other questions?

Here are some related questions:

  1. What is the degree of this polynomial?
  2. How do you identify the leading coefficient in a polynomial?
  3. What is the significance of the leading term in a polynomial?
  4. How do you find the roots of this polynomial?
  5. How do you factor this polynomial?
  6. How does the leading term affect the end behavior of the polynomial?
  7. Can the polynomial be simplified further?
  8. What are the turning points of this polynomial?

Tip: In polynomials, the leading term (the term with the highest power) is crucial in determining the behavior of the function as xx approaches positive or negative infinity.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Polynomials
Degree of a polynomial
Leading term
Coefficient

Formulas

-

Theorems

-

Suitable Grade Level

Grades 10-12