Question

Let f (x) be a fourth degree polynomial with coefficient of x^4 is 1 is such that f(-1)=1, f(2)=3 , f(-3)=9, f(4)= 16 ,then find f(1).

Answer 1

Let the polynomial be 
$f(x) = x^{4} + ax^3 + bx^2 + cx + d$

f(-1) = 1
1 - a + b -c +d = 1
a - b + c - d = 0...........(1)

f(2) = 3
16 +8a + 4b + 2c + d = 3  
8a + 4b + 2c + d = -13 ............(2)

f(-3) = 9
81 - 27a + 9b - 3c + d = 9   
- 27a + 9b - 3c + d = -72 ............(3)  

f(4) = 16
256 + 64a + 16b + 4c + d = 16   
64a + 16b + 4c + d = -240 ............(4)

Solving these 4 equations, we get the values of a, b c and d. Then find the value of f(1). 

I just left the answer in the midway, so that you will try on your own.