Question

What is the name of the polynomial x³-8x²+19?

1) Cubic polynomial
2) Quadratic polynomial
3) Linear polynomial
4) Constant polynomial

Answer 1

The polynomial x^3 - 8x^2 + 19 is a cubic polynomial because its highest degree term is cubic (x^3).

Step-by-step explanation:

The name of the polynomial x3 - 8x2 + 19 is a cubic polynomial. This is because the highest degree of any term in the polynomial is 3, which corresponds to the cubic term x3. The reference to The Solution of Quadratic Equations and the term quadratic functions mentions polynomials of the form ax2 + bx + c = 0, which are known as second-order polynomials. In contrast, our given polynomial is not of this form since it contains a third power of x, making it cubic, not quadratic. Therefore, option 1, Cubic polynomial, is the correct answer to the question.