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Select the correct answer.(\newline\)What is the degree of the polynomial function (\newline\) $f(x)=2x^{3}+7x^{2}-4x-12$ ,(\newline\)A. $3$ (\newline\)B. $5$ (\newline\)C. $2$ (\newline\)D. $13$

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Find derivatives using the quotient rule I

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Q. Select the correct answer.(\newline\)What is the degree of the polynomial function (\newline\)

f(x)=2x^{3}+7x^{2}-4x-12

,(\newline\)A.

3

(\newline\)B.

5

(\newline\)C.

2

(\newline\)D.

13

Definition of Degree: The degree of a polynomial is the highest power of the variable $x$ that appears in the polynomial with a non-zero coefficient.
Combine Like Terms: First, we combine like terms in the polynomial $f(x) = 2x^3 + 7x^3 - 4x - 12$ . The like terms here are the terms with $x^3$ .
Simplify Polynomial: Combining the like terms gives us $f(x) = (2x^3 + 7x^3) - 4x - 12$ , which simplifies to $f(x) = 9x^3 - 4x - 12$ .
Identify Highest Power: Now that we have simplified the polynomial, we can see that the highest power of $x$ is $3$ in the term $9x^3$ .
Degree of Polynomial: Therefore, the degree of the polynomial $f(x) = 9x^3 - 4x - 12$ is $3$ .

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