Math Problem Statement
Answer the questions about the following polynomial. 1, minus, 3, x, cubed 1−3x 3
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 . Let's analyze it step by step to answer the questions:
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Number of Terms:
The polynomial consists of two terms: (the constant term) and (the cubic term). Therefore, this is a polynomial with 2 terms. -
Constant Term:
The constant term is the term that does not contain the variable . In this polynomial, the constant term is . -
Leading Term:
The leading term of a polynomial is the term with the highest power of . Here, the term with the highest power of is . Thus, the leading term is . -
Leading Coefficient:
The leading coefficient is the coefficient of the leading term. For the term , the coefficient is . Hence, the leading coefficient is .
To summarize:
- The polynomial represents a polynomial with 2 terms.
- The constant term is 1.
- The leading term is .
- The leading coefficient is .
Would you like more details or have any questions?
Here are some related questions for further exploration:
- What is the degree of the polynomial ?
- How would the behavior of the polynomial change if the leading coefficient was positive?
- Can the polynomial be factored further?
- What are the roots of the polynomial equation ?
- How would the graph of look, and where would it intersect the y-axis?
Tip: Remember, the leading term and leading coefficient play a crucial role in determining the end behavior of the polynomial's graph.
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Math Problem Analysis
Mathematical Concepts
Polynomials
Formulas
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Theorems
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Suitable Grade Level
Grades 7-9
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