Finding a possible degree and L.C. of a polynomial function?

[kendang]

Question:
The finite difference of a polynomial function, whose leading coefficient is a whole number, is 144. What can the possible degrees and leading coefficients of this function be? Justify your answer with appropriate calculations and a brief explanation.

From what I know:

A polynomial function is in the form of y=ax^n+b[/*:m:kotsojkk]
Finite difference are difference from the "y" values when x is subbed into "f(x"), which is given as: 144.[/*:m:kotsojkk]
The "a" value is a whole number.[/*:m:kotsojkk]


How can I find suitable degrees and leading coefficients when I do not know function?

[tkhunny]

144*x

72*x^2

24*x^3

6*x^4

We still need a better defintion of "finite difference". It should be a rather general term and you are using it for a much more specific purpose. Very confusing.

[JeffM]

Question:
The finite difference of a polynomial function, whose leading coefficient is a whole number, is 144. What can the possible degrees and leading coefficients of this function be? Justify your answer with appropriate calculations and a brief explanation.

From what I know:

A polynomial function is in the form of y=ax^n+b No A polynomial of degree n has the general form a[sub:3qi3pwpj]1[/sub:3qi3pwpj]x[sup:3qi3pwpj]n[/sup:3qi3pwpj] + a[sub:3qi3pwpj]2[/sub:3qi3pwpj]x[sup:3qi3pwpj]n-1[/sup:3qi3pwpj] + ... a[sub:3qi3pwpj]n[/sub:3qi3pwpj]x[sup:3qi3pwpj]1[/sup:3qi3pwpj] + a[sub:3qi3pwpj]n+1[/sub:3qi3pwpj]x[sup:3qi3pwpj]0[/sup:3qi3pwpj] [/*:m:3qi3pwpj]
Finite difference are difference from the "y" values when x is subbed into "f(x"), which is given as: 144. Generally a finite difference is defined with respect to two values of x such as f(x + a) - f(x + b). [/*:m:3qi3pwpj]
The "a" value is a whole number. In my notation a[sub:3qi3pwpj]1[/sub:3qi3pwpj] is a whole number[/*:m:3qi3pwpj]


How can I find suitable degrees and leading coefficients when I do not know function?