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(x^2+4x+3)x^2+(x^2+4x+3)3x+2(x^2+4x+3)

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1 Answer

     (x2 + 4x + 3)x2 + (x2 + 4x + 3)3x + 2(x2 + 4x + 3)

==>   x2(x2 + 4x + 3) + 3x(x2 + 4x + 3) + 2(x2 + 4x + 3)

Notice that all terms here share a common factor, that being   x2 + 4x + 3 . So if we factor out this trinomial from each term, we are left with the following:

     (x2 + 4x + 3)(x2 + 3x + 2)

Next, factor each trinomial:

     (x + 1)(x + 3)(x + 1)(x + 2)

     (x + 1)(x + 1)(x + 2)(x + 3)

     (x + 1)1+1(x + 2)(x + 3)

     (x + 1)2(x + 2)(x + 3)