To name the polynomial [tex]\(18x^3 + 11x^2 - 14x\)[/tex], we need to determine the highest degree term in the polynomial. The degree of a polynomial is the highest power of [tex]\(x\)[/tex] present in the polynomial.
Let's examine each term:
- The term [tex]\(18x^3\)[/tex] has a degree of 3.
- The term [tex]\(11x^2\)[/tex] has a degree of 2.
- The term [tex]\(-14x\)[/tex] has a degree of 1.
Among these terms, the highest degree is 3.
A polynomial is typically named according to its highest degree:
- A polynomial of degree 1 is called a linear polynomial.
- A polynomial of degree 2 is called a quadratic polynomial.
- A polynomial of degree 3 is called a cubic polynomial.
- And so forth.
Given that the highest degree term in our polynomial is 3, the polynomial [tex]\(18x^3 + 11x^2 - 14x\)[/tex] is a cubic polynomial.
Therefore, the name of the polynomial [tex]\(18x^3 + 11x^2 - 14x\)[/tex] is a cubic polynomial.
