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 . Let's analyze it step-by-step.
- Type of Polynomial: Since this polynomial has one term with a variable, it is a linear polynomial.
- Number of Terms: This polynomial has 2 terms (the terms are and ).
- Constant Term: The constant term in the polynomial is -1.
- Leading Term: The leading term (the term with the highest power of ) is 3x.
- Leading Coefficient: The coefficient of the leading term (the coefficient of ) 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:
- What distinguishes a linear polynomial from higher-degree polynomials?
- How would the answers change if the polynomial were instead?
- What role does the constant term play in the graph of a polynomial?
- How can you determine the degree of a polynomial just by looking at the terms?
- 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 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