- #1
Mathsig
- 1
- 0
- TL;DR Summary
- 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.
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:Why is a third degree polynomial called a cubic polynomial?
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.
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.
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.
A cubic polynomial has the following characteristics:
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.