Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=3x^2+5x+2$

• A. Polynomial with $n=3,a_{n}=2$
• B. Polynomial with $n=2,a_{n}=3$
• C. Polynomial with $n=2,a_{n}=2$
• D. Not a polynomial function.

Answer: (B)

Verified step by step guidance

1. Identify the given function: \( f(x) = 3x^2 + 5x + 2 \).
2. Check if the function is a polynomial: A polynomial function is an expression consisting of variables and coefficients, involving only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
3. Since \( f(x) = 3x^2 + 5x + 2 \) involves only non-negative integer exponents (2 and 1) and operations of addition and multiplication, it is a polynomial function.
4. Write the polynomial in standard form: The standard form of a polynomial arranges the terms in descending order of their exponents. The given function is already in standard form: \( 3x^2 + 5x + 2 \).
5. Determine the degree and leading coefficient: The degree of a polynomial is the highest exponent of the variable, which is 2 in this case. The leading coefficient is the coefficient of the term with the highest degree, which is 3.