If x=-2,1,2 and the y intercept is y=-8 for y=ax^3+bx^2+cx+d, what is a, b, c and d

a=-2, b=2, c=8, d=-8We know d=-8 from the y interception setting x=0 and y=-8For a, b and c we must construct 3 simultaneous equations from the given information x=-2, 1 and 21.) -8a+4b-2c=82.) a+b+c=83.) 8a+4b+2c=8from 1.) and 3.) we get 8b=16 so b=2from 1.) and 2.) we get 12b + 6c=72 so c=8and from 2.) we get a+2+8=8 so a=-2Check by subbing in x=-2 we get y=0 as required.