Question

f(x) is polynomial in x with the following functions value : f(2)=f(3)=27, f(4)= 78, f(5) =169. the (x) = ?
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Answer 1

Step-by-step explanation:

Start with f(x) = ax^3 + bx^2 + cx + d plug in x = 2, 3, 4, 5 : you will have 4 equations in in 4 unknowns , solve and Done!

f(2) : 8a + 4b +2c + d = 27

f(3): 27a + 9b + 3c + d = 27

f(4): 64a + 16b + 4c + d = 78

f(5): 125a + 25b + 5c + d = 169

I leave the Solving for the readers { just eliminate one by one and then Solve}