If you did it correctly, you should have (x^7 + x^6 + x^3 + x^2)*(x^3 + x^2 + 1) = (x^4 + x + 1).

(x^7 + x^6 + x^3 + x^2)*(x^3 + x^2 + 1) =

(x^10 + x^9 + x^6 + x^5)+(x^9 + x^8 + x^5 + x^4)+(x^7 + x^6 + x^3 + x^2) =

x^10 + x^8 + x^7 + x^4 + x^3 + x^2 =

x^8 + x^7 + x^6 + x^5 + x^4 =

x^7 + x^6 + x^5 + x^3 + x + 1

which is not x^4 + x + 1.

I get (x^4 + x + 1)*(x^4 + x^3 + x + 1) =

(x^8 + x^7 + x^5 + x^4)+(x^5 + x^4 + x^2 + x)+(x^4 + x^3 + x + 1) =

x^8 + x^7 + x^4 + x^3 + x^2 + 1 =

x^7 + x^2 + x

Which is the correct answer, since:

(x^7 + x^6 + x^3 + x^2)*(x^7 + x^2 + x) =

(x^14 + x^13 + x^10 + x^9)+(x^9 + x^8 + x^5 + x^4)+(x^8 + x^7 + x^4 + x^3) =

x^14 + x^13 + x^10 + x^7 + x^5 + x^3 =

x^13 + x^9 + x^6 + x^5 + x^3 =

x^8 + x^3 =

x^4 + x + 1

- Hollywood