SOLUTION: If f is a polynomial of degree 4 such that f(0) = f(1) = f(2) = f(3) = 1 and f(4) = 0, then determine f(5).

Question 1077691: If f is a polynomial of degree 4 such that
f(0) = f(1) = f(2) = f(3) = 1
and
f(4) = 0,
then determine f(5).
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

�> (use e=1 in evaluating f(1)�f(4) below)
�> �>
�> �>
�> ... �>
�> � �>
�
This generates the following matrix (moving constants to right hand side):
�

The inverse of the 4x4 matrix is (from https://www.symbolab.com/solver/matrix-inverse-calculator )

--
And the solution we seek is:

pull out 1/24:

�
Now we are ready to find f(5):

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