SOLUTION: the value of the expression x^4-17x^3+17x^2-17x+17 at x =16 is ???? I know substitution but it consumes lot of time some shortcuts please.

Algebra ->  Equations -> SOLUTION: the value of the expression x^4-17x^3+17x^2-17x+17 at x =16 is ???? I know substitution but it consumes lot of time some shortcuts please.       Log On


   

Question 622722: the value of the expression x^4-17x^3+17x^2-17x+17 at x =16 is ????
I know substitution but it consumes lot of time some shortcuts please.
Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
the value of the expression x^4-17x^3+17x^2-17x+17 at x =16 is ????
I know substitution but it consumes lot of time some shortcuts please.
----------
There's no shortcut to my knowledge.
-----
If you want to evaluate a function at several points, make an Excel sheet.
------
You can dl FREE graph software at
http://www.padowan.dk
that will graph the function and will evaluate it at any point, too.
Using that, f(16) = 1

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
By the Remainder Theorem we know that f(a) = the remainder of f%28x%29%2F%28x-a%29. And we can use synthetic division to divide:
16 |    1   -17    17    -17    17
====         16   -16     16   -16
       ===========================
        1    -1     1    -1      1

The number in the lower right corner is the remainder. So x%5E4-17x%5E3%2B17x%5E2-17x%2B17 is 1 at x = 16. This may not be very simple but it is probably easier than raising 16 to all those different powers.