Determine whether F(x) represents a polynomial function. If it is, state its degree and leading coefficient.

Question

Determine whether F(x) represents a polynomial function. If it is, state its degree and leading coefficient.

 

f(x) = 9 - 8x

 

is f(x) a polynomial function?

 

 

A. the function is a polynomial function with leading coefficient  ?  and degree ?

 

or

 

B. the function is not a polynomial function.

Answer 1

A Polynomial Function is the sum of one or more Terms where each Term is either a number, or a number times the independent variable raised to a positive integer exponent.

 

The Degree of a Term is the value of the exponent of the variable, or zero if no variable is present.

 

The Degree of the Function is the largest Term Degree.

 

Terms with the same Degree are combined using the Distributive Property.

 

Terms are usually listed in decreasing Degree.

 

In general, an n^th degree polynomial function of x is written:

 

f(x) = a_n xⁿ + a_n–1 x^n-1 + a_n-2 x^n-2 + ... + a₁ x + a₀

 

where the Leading Coefficient is a_n.

 

So f(x) = 9 - 8x is a polynomial function of x that is not in conventional order. The Leading Coefficient is –8 and the largest Term Degree is 1, so the polynomial function Degree is 1.

Answer 2

A polynomial function means it can be written is the form Ax² + Bx + C. As we can see it is in the form.  Where A,B, and C are coefficients. 

In this case f(x)= 9-8x. So the coefficient is -8 with a degree of 1. Hope this helps!