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Questions and Answers
What is the degree of the polynomial 2x^3 - 5x^2 + x - 1?
What is the degree of the polynomial 2x^3 - 5x^2 + x - 1?
What can be determined by the degree of a polynomial?
What can be determined by the degree of a polynomial?
What is the degree of the polynomial x^2 - 4x + 2?
What is the degree of the polynomial x^2 - 4x + 2?
What type of polynomial is 5?
What type of polynomial is 5?
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What determines the shape of the graph of a polynomial?
What determines the shape of the graph of a polynomial?
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What is the degree of the polynomial 3x^4 + 2x^2 - 5?
What is the degree of the polynomial 3x^4 + 2x^2 - 5?
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Study Notes
Degree of a Polynomial
The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.
Key Points:
- The degree of a polynomial is a non-negative integer.
- The degree of a polynomial is the largest exponent of the variable in the polynomial.
- A polynomial with degree 0 is a constant polynomial.
- A polynomial with degree 1 is a linear polynomial.
- A polynomial with degree 2 is a quadratic polynomial.
- A polynomial with degree 3 is a cubic polynomial.
Examples:
- The polynomial
3x^4 + 2x^2 - 5has a degree of 4, because the highest power of x is 4. - The polynomial
x^2 - 4x + 2has a degree of 2, because the highest power of x is 2. - The polynomial
5has a degree of 0, because it is a constant polynomial.
Importance of Degree:
- The degree of a polynomial determines the number of roots or solutions it can have.
- The degree of a polynomial also determines the shape of its graph.
- Polynomials of different degrees have different properties and behaviors.
Degree of a Polynomial
- The degree of a polynomial is the highest power of the variable (usually x) in the polynomial.
Key Points
- The degree of a polynomial is a non-negative integer.
- The degree of a polynomial is the largest exponent of the variable in the polynomial.
- Polynomials can have different degrees, including:
- 0, which is a constant polynomial.
- 1, which is a linear polynomial.
- 2, which is a quadratic polynomial.
- 3, which is a cubic polynomial.
Examples
- The highest power of x in the polynomial
3x^4 + 2x^2 - 5is 4, making its degree 4. - The highest power of x in the polynomial
x^2 - 4x + 2is 2, making its degree 2. - The polynomial
5has a degree of 0, because it is a constant polynomial.
Importance of Degree
- A polynomial's degree determines the number of roots or solutions it can have.
- The degree of a polynomial determines the shape of its graph.
- Polynomials of different degrees have different properties and behaviors.
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Description
Understand the concept of degree in polynomials, including how to find the degree and the different types of polynomials based on their degree.
