Question 562138
The polynomial must have factors {{{x-(-2)}}}={{{x+2}}},
{{{(x-1)^2}}}, and {{{x-3}}}.
If it is a polynomial of degree 4, it will be
{{{P(x)=a(x+2)(x-1)^2(x-3)}}}
If we also know that {{{P(-4)=210}}}
{{{P(-4)=a(-4+2)(-4-1)^2(-4-3)=a(-2)(-5)^2(-7)=2*25*7*a=350a=210}}},
then {{{a}}}={{{210/350}}}={{{3/5}}}
{{{P(x)=(3/5)(x+2)(x-1)^2(x-3)}}}={{{(3/5)(x^4-3x^3-3x^2+11x-6)}}}
There are also infinite other polynomials with the same roots passing through the same point. For example,
{{{G(x)=(3/10)(x^2+4)(x+2)(x-1)^2(x-3)}}} has exactly the same roots and complies with {{{G(-4)=210}}}, but its degree is 6,and it's probably not the intended answer.