100 points, !
suppose p is a monic quartic polynomial (i. e. a 4th-degree polynomial with leading coefficient 1) such that p(1)=1, p(2)=4, p(3)=9, p(4)=16. find p(5).

  P(5) = 49

Step-by-step explanation:

A graphing calculator shows the quartic function that matches the given points is ...

P(x) = x^4 -10x^3 +36x^2 -50x +24

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Evaluating for x=5, we have ...

  P(5) = (((5 -10)5 +36)5 -50)5 +24 = ((-25+36)5 -50)5 +24 = (55 -50)5 +24

  P(5) = 49

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