Math Problem Statement

Answer the questions about the following polynomial: 3x - 1. The expression represents a [ ] polynomial with [ ] terms. The constant term is [ ], the leading term is [ ], and the leading coefficient is [ ].

Solution

The polynomial provided is 3x13x - 1. Let's analyze it step-by-step.

  1. Type of Polynomial: Since this polynomial has one term with a variable, it is a linear polynomial.
  2. Number of Terms: This polynomial has 2 terms (the terms are 3x3x and 1-1).
  3. Constant Term: The constant term in the polynomial is -1.
  4. Leading Term: The leading term (the term with the highest power of xx) is 3x.
  5. Leading Coefficient: The coefficient of the leading term (the coefficient of xx) is 3.

So, the answers are:

  • Type of polynomial: linear
  • Number of terms: 2
  • Constant term: -1
  • Leading term: 3x
  • Leading coefficient: 3

Would you like further details or have any questions?


Here are 5 related questions for further exploration:

  1. What distinguishes a linear polynomial from higher-degree polynomials?
  2. How would the answers change if the polynomial were 3x213x^2 - 1 instead?
  3. What role does the constant term play in the graph of a polynomial?
  4. How can you determine the degree of a polynomial just by looking at the terms?
  5. What is the significance of the leading coefficient in the behavior of polynomial functions?

Tip: For linear polynomials, the leading term is always the term with xx raised to the first power, making the polynomial degree 1.

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Math Problem Analysis

Mathematical Concepts

Polynomial
Linear Polynomial
Terms of a Polynomial
Coefficient

Formulas

None required for identification of terms and coefficients in a polynomial

Theorems

None required for this basic polynomial identification problem

Suitable Grade Level

Grades 6-8