Let
[tex] A (-4, 89) B (-3, 7)C (-1, -1) D (1, -1)E (4, 329) [/tex]
Using a graph tool
case a) [tex] y = 2x^{3}-3x^{2}-2x + 1 [/tex]
see the attached figure N [tex] 1 [/tex]
The polynomial is not the solution
case b) [tex] y = x^{4}-2x^{3}-3x^{2} + 2x+1 [/tex]
see the attached figure N [tex] 2 [/tex]
The polynomial is not the solution
case c) [tex] y = x^{4}-2x^{3}+3x^{2} + 2x-1 [/tex]
see the attached figure N [tex] 3 [/tex]
The polynomial is not the solution
case d) [tex] y = x^{4}+2x^{3}-3x^{2} - 2x+1 [/tex]
see the attached figure N [tex] 4 [/tex]
The polynomial pass through all the points
therefore
the answer is the polynomial
d) [tex] y = x^{4}+2x^{3}-3x^{2} - 2x+1 [/tex]
