+237 Let P(x) be a polynomial whose degree is 3. If P(1) = 1, P(2) = 3, P(3) = 2, and P(4) = 10, compute the value P(5).
+128475 This is similar to this problem I just worked :
https://web2.0calc.com/questions/if-f-is-a-polynomial-of-degree-3-such-that-f-0-f_1
We have this system
a + b + c + d = 1
8a + 4b + 2c + d = 3
27a + 9b + 3c + d = 2
64a +16b + 4c + d =10
Time doesn't permit me to go through the solving process (it isn't difficult, just tedious) but WoframAlpha gives the solutions:
a =2, b = -27/2 c =57/2 d = -16
Our polynomial is f(x) = 2x^3 - (27/2)x^2 + (57/2)x - 16
P(5) = 39
See the graph here : https://www.desmos.com/calculator/6t4hhafji0
