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Mathsig
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- Why is third degree called cubic?
Why is a third degree polynomial called a cubic polynomial? I just don’t see the connection between 3 and a cube.
Why Is a Cubic Polynomial Called 'Third Degree'?
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In summary, the names of polynomial functions are based on the geometric shapes that correspond to their degree. The third degree polynomial is called a cubic polynomial because its graph resembles a three-dimensional cube, and its volume formula is based on the cube's side length raised to the third power.
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A cube is a three dimensional object. The volume of a cube is ##l^3##, where ##l## is the side length. That's cubic formula, in both senses.
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russ_watters
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It's the same reason the second degree is square.
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Mark44
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Further, a second degree polynomial is called a quadratic polynomial because the area of a square is ##l^2##. The Latin word quadratus means "square."Mathsig said:
Other types of polynomials have names such as quartic (fourth degree) and quintic (fifth degree).
1. Why is a cubic polynomial called 'third degree'?
A cubic polynomial is called 'third degree' because it is a polynomial of degree 3. This means that the highest power of the variable in the polynomial is 3. The term 'third degree' comes from the fact that the polynomial has 3 terms, each with a different power of the variable.
2. How is the degree of a polynomial determined?
The degree of a polynomial is determined by looking at the highest power of the variable in the polynomial. For example, in the polynomial 3x^2 + 5x + 2, the highest power of x is 2, so the degree of the polynomial is 2. In the case of a cubic polynomial, the highest power of the variable is 3, hence it is called third degree.
3. What is the significance of the degree of a polynomial?
The degree of a polynomial is important because it tells us the maximum number of solutions or roots that the polynomial can have. For example, a quadratic polynomial (degree 2) can have a maximum of 2 solutions, while a cubic polynomial (degree 3) can have a maximum of 3 solutions. The degree also helps us in determining the end behavior of the polynomial graph.
4. What are the characteristics of a cubic polynomial?
A cubic polynomial has the following characteristics:
- It is a polynomial of degree 3
- It has 3 terms, each with a different power of the variable
- It has at most 3 solutions or roots
- Its graph is a smooth curve with no sharp turns
5. Can a polynomial with a degree higher than 3 be called a 'third degree' polynomial?
No, a polynomial with a degree higher than 3 cannot be called a 'third degree' polynomial. The term 'third degree' specifically refers to polynomials of degree 3. Polynomials with a higher degree are referred to as 'higher degree' polynomials.
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