Question

decide whether $f(x) = -3x + 5x^3 - 6x^2 + 2$ is a polynomial function.
polynomial function
not a polynomial function
if the function is a polynomial function, write it in standard form and state its degree, type and leading coefficient. if not, leave each response blank.
$f(x) = \square$
degree:
type:
leading coefficient:

Explanation:

Step1: Define polynomial function

A polynomial function has the form $a_nx^n+...+a_1x+a_0$, where exponents are non-negative integers, coefficients are real numbers.

Step2: Verify given function

For $f(x)=-3x+5x^3-6x^2+2$, all exponents (3,2,1,0) are non-negative integers, coefficients are real. So it is a polynomial.

Step3: Write in standard form

Arrange terms by descending exponents: $f(x)=5x^3-6x^2-3x+2$

Step4: Identify degree

Degree is highest exponent: $3$

Step5: Identify type

Degree 3 polynomial is cubic.

Step6: Identify leading coefficient

Coefficient of highest degree term: $5$

Answer:

polynomial function
$f(x)=5x^3-6x^2-3x+2$
degree: $3$
type: cubic polynomial function
leading coefficient: $5$