Q1: You can use finite differences to determine the leading coefficient of any polynomial function. Determine the relation that exists between the nth finite difference and the leading coefficient, a, for the general polynomial function.
f(x) = a[sub:3igctqvy]n[/sub:3igctqvy]x[sup:3igctqvy]n[/sup:3igctqvy] + a[sub:3igctqvy]n-1[/sub:3igctqvy]x[sup:3igctqvy]n-1[/sup:3igctqvy] +...+ a[sub:3igctqvy]2[/sub:3igctqvy]x[sup:3igctqvy]2[/sup:3igctqvy] + a[sub:3igctqvy]1[/sub:3igctqvy]x + a0
I don't understand the relationship between those too.. .the answer at the back of the book says "a[sub:3igctqvy]n[/sub:3igctqvy]n!", which i also dont understand
Q2: The polynomial f(x) = ax[sup:3igctqvy]5[/sup:3igctqvy] + 3x[sup:3igctqvy]4[/sup:3igctqvy] - 2x[sup:3igctqvy]3[/sup:3igctqvy] - 3x[sup:3igctqvy]2[/sup:3igctqvy] + x - 1 has a common difference of -120. What is the value of a?
Because i didnt understand the relationship, I couldn't solve the second problem either. the answer at the back of the book states "-1"
I will appreciate your help
Thank you!
f(x) = a[sub:3igctqvy]n[/sub:3igctqvy]x[sup:3igctqvy]n[/sup:3igctqvy] + a[sub:3igctqvy]n-1[/sub:3igctqvy]x[sup:3igctqvy]n-1[/sup:3igctqvy] +...+ a[sub:3igctqvy]2[/sub:3igctqvy]x[sup:3igctqvy]2[/sup:3igctqvy] + a[sub:3igctqvy]1[/sub:3igctqvy]x + a0
I don't understand the relationship between those too.. .the answer at the back of the book says "a[sub:3igctqvy]n[/sub:3igctqvy]n!", which i also dont understand
Q2: The polynomial f(x) = ax[sup:3igctqvy]5[/sup:3igctqvy] + 3x[sup:3igctqvy]4[/sup:3igctqvy] - 2x[sup:3igctqvy]3[/sup:3igctqvy] - 3x[sup:3igctqvy]2[/sup:3igctqvy] + x - 1 has a common difference of -120. What is the value of a?
Because i didnt understand the relationship, I couldn't solve the second problem either. the answer at the back of the book states "-1"
I will appreciate your help
Thank you!