When a graph just "kisses" the x axis, we will have 2n zeroes at that point
So...let's assume that x = 2 we have two zeroes
Thus, let us guess that (x - 2)^2 = x^2 - 4x + 4 divides the polynomial
3x^2 + x + 2
x^2 - 4x + 4 [ 3x^4 -11x^3 + 10x^2 - 4x + 8 ]
3x^4 -12x^3 + 12x^2
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x^3 - 2x^2 - 4x + 8
x^3 - 4x^2 + 4x
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2x^2 - 8x + 8
2x^2 - 8x + 8
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So...the factorization is ( 3x^2 + x + 2 ) ( x - 2) ^2