Polynomials and second derivatives

Find a polynomial p so that:

p''(t)+3p'(t) + 2p(t) = (t^2)-2

for all numbers t.

(note: p''= p double prime and t^2 = t raised to the power of 2)

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...3*a3*t^2+...+n*an*t^(n-1)
p''(t)=2*a2+6*a3*t+...+n*(n-1)*t^(n-2)

From p''(t)+3p'(t) + 2p(t) = (t^2)-2, we have

(2*a2+6*a3*t+...n*(n-1)*t^(n-2))+3* ( a1+2*a2*t+3*a3*t^2+...+n*an*t^(n-1) ) +2* (a0+ a1*t+a2*t^2+a3*t^3+...+an*t^n) =(t^2)-2

Now we compare the coefficients of ...