Math Problem Statement

Name the degree, the leading coefficient, and the constant: f(x)= -x6 + 2x3 – x + 3. Write the answer in the order listed in the question(degree first, then leading coefficient, then constant value)

Column A 1. 6: 6 2. -1: -1 3. 3: 3 Column B a. leading coefficient b. constant value c. degree

Solution

For the function f(x)=x6+2x3x+3f(x) = -x^6 + 2x^3 - x + 3:

  1. Degree: 6
  2. Leading Coefficient: -1
  3. Constant Value: 3

So the answer in the requested order is:

6, -1, 3.

Column Matching:

  • 6: (c) degree
  • -1: (a) leading coefficient
  • 3: (b) constant value

Do you want more details or have any questions? Here are some related questions you might consider:

  1. What is the significance of the leading coefficient in polynomial functions?
  2. How do you determine the degree of a polynomial?
  3. Can you explain what a constant term represents in a polynomial?
  4. How does the degree of a polynomial affect its graph?
  5. What happens to the behavior of the function as xx approaches infinity or negative infinity based on its degree?

Tip: Understanding the degree and leading coefficient helps predict the behavior of polynomial functions.

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Math Problem Analysis

Mathematical Concepts

Polynomial Functions
Algebra

Formulas

f(x) = ax^n + ...
Degree of a polynomial

Theorems

Properties of polynomial functions

Suitable Grade Level

Grades 9-11