Question

decide whether ( f(x) = -3x + 5x^3 - 6x^2 + 2 ) is a polynomial function.
options:

• 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.

Explanation:

Step1: Identify polynomial eligibility

A polynomial function has non-negative integer exponents on the variable, which $f(x) = -3x + 5x^3 - 6x^2 + 2$ satisfies.

Step2: Rearrange to standard form

Standard form orders terms by descending exponents:
$5x^3 - 6x^2 - 3x + 2$

Step3: Find degree, type, leading coefficient

Degree = highest exponent = 3; Type = cubic polynomial; Leading coefficient = coefficient of $x^3$ = 5.

Answer:

• The function is a polynomial function.
• Standard form: $f(x)=5x^3 - 6x^2 - 3x + 2$
• Degree: $3$
• Type: Cubic polynomial function
• Leading coefficient: $5$