SOLUTION: How do I determine the polynomial function of least degree whose graph passes through the given points (−1, 2), (0, 0), (1, 1), (4, 58), p(x)=? Thank you!!!

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Question 896428: How do I determine the polynomial function of least degree whose graph passes through the given points (−1, 2), (0, 0), (1, 1), (4, 58), p(x)=?
Thank you!!!

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
One root of p is zero, so you can begin with , to try to find a CUBIC polynomial.

The other three points let you form a system of three equations.


-
-
, using (-1,2).

, using (1,1).



, using point (4,58).

Solve for the coefficients a, b, c in the system




R2+R1, and R3+32*R1,



R3-20*R2
and one small division of R3 by constant, scaler



Which indicates .
Using that continuing without further matrix operations,
and .

Putting this all into expected cubic p(x),
.
This was not checked but it should be checked.

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