sub in each of the points to get
-4 = 0+0+0+d , so we know d = -4
-8 = a+b+c - 4 ---> a+b+c = -4
-8 = -a + b -c-4 ---> -a + b-c = -4
let's add these last two : 2b = -8 or b = -4
-2 = 8a +4b + 2c - 4
8a -16 + 2c - 4 = 2
4a -8 + c = 1 or c = -4a+9
sub into a+b+c=-4
a -4 + (-4a + 9) = -4
-3a = -9
a=3 and finally c = -12+9 = -3
so f(x) = 3x^3 -4x^2 - 3x - 4
I will leave it up to you to sub in the given points, I think they all work
BTW, the above is not the only way to do it, I sort of just let it flow.
Solve the system:
Add the 2nd and the 3rd: 2b+2d=-16
Subtract from the 4th 2*3rd: 6a=18
a=3, b=-4, c=-3, d=-4
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