Math Problem Statement
Answer the questions about the following polynomial. 1, minus, 3, x, cubed 1−3x 3
Answer Attempt 1 out of 2
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 based on the components mentioned in the question.
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Polynomial type and number of terms:
The polynomial has two terms: (the constant term) and (the cubic term). Therefore, this is a binomial because it has exactly two terms. -
Constant term:
The constant term in the polynomial is . This is the term that does not contain the variable . -
Leading term:
The leading term of a polynomial is the term with the highest power of . In this polynomial, the term with the highest power of is . Therefore, 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 .
In summary:
- The polynomial is a binomial 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 polynomial change if the leading coefficient was positive?
- What are the roots of the polynomial ?
- How would you graph the polynomial ?
- What happens to the polynomial if a linear term (e.g., ) is added?
Tip: The degree of a polynomial is determined by the highest power of the variable present in the expression.
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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