Find a polynomial of the form f(x)=ax^3+bx^2+cx+d such that f(0)=−5, f(−2)=6, f(4)=5, and f(−5)=−3. f(x) = ?

Answer 1

sigh. only brute force will do. plug in your points to get
d = -5
-8a+4b-2c+d = 6
64a+16b+4c+d = 5
-125a+25b-5c+d = -3
since we know d=5, that gives us
-8a+4b-2c = 11
64a+16b+4c = 10
-125a+25b-5c = 2
now solve as usual