QuestionClassify the polynomial $9 f^{3}-9 f$ : cubic, quadratic, linear, or none of these?

Studdy Solution

STEP 1

Assumptions1. The given expression is a polynomial. . The expression is in standard form, meaning the terms are arranged in descending order of their degree.

STEP 2

A polynomial is classified based on its degree. The degree of a polynomial is the highest power of the variable in the polynomial.

STEP 3

In the given polynomial, identify the terms and their respective degrees.
The given polynomial is $9 f^{3}-9 f$ The first term is $9f^3$ and its degree is3. The second term is $-9f$ and its degree is1.

STEP 4

The degree of the polynomial is the highest degree among all its terms.
In this case, the highest degree is3.

STEP 5

Classify the polynomial based on its degree.
A polynomial of degree1 is called a linear polynomial. A polynomial of degree2 is called a quadratic polynomial. A polynomial of degree3 is called a cubic polynomial.
Since the degree of the given polynomial is3, it is a cubic polynomial.
So, the given polynomial $9 f^{3}-9 f$ is a cubic polynomial.

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