Answer:
[tex]f(x) = {x}^{4} +4 {x}^{3} + 3 {x}^{2} [/tex]
Step-by-step explanation:
Let f(x) be the polynomial.
If x=-3, x=0,x=0, x=1 are roots ,then by the factor theorem, x+3=0,x=0,x=0, x+1=0 are factors of f(x).
This implies that:
[tex]f(x) = (x + 3)(x)(x)(x + 1)[/tex]
[tex]f(x) = {x}^{2} ( {x}^{2} + x + + 3x + 3)[/tex]
[tex]f(x) = {x}^{2} ( {x}^{2} +4x + 3)[/tex]
Expand further to get:
[tex]f(x) = {x}^{4} +4 {x}^{3} + 3 {x}^{2} [/tex]
