Question

100 points, please help!

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).

Answer 1

P(5) = 49

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

Answer 2

P(5) = 49

Explanation:

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

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

___

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