Phân tích thành nhân tử: a) x^4+5x^3+9x^2+7x+2 b) (x^4+4x+8)+3x(x4+4x+8)+2x^2 c) 2x^2-7x+5y^2

Phân tích thành nhân tử:
a) x^4+5x^3+9x^2+7x+2
b) (x^4+4x+8)+3x(x4+4x+8)+2x^2
c) 2x^2-7x+5y^2

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  1. $\begin{array}{l}a)\,\,x^4+5x^3+9x^2+7x+2\\= x^4 + 2x^3 + 3x^3 + 6x^2 + 3x^2 + 6x + x + 2\\= x^3(x + 2) + 3x^2(x +2) + 3x(x + 2) + (x + 2)\\=(x +2)(x^3 + 3x^2 + 3x + 1)\\= (x +2)(x +1)^3\\b)\,\,(x^4 + 4x + 8)^2 + 3x(x^4 + 4x + 8) + 2x^2\\= (x^4+4x+8)^2+x(x^4+4x+8)+2x(x^4 + 4x + 8) + 2x^2\\= (x^4 +4x + 8)(x^2 + 5x +8)+ 2x(x^4 + 5x + 8)\\= (x^4 + 5x + 8)(x^4 + 6x + 8)\\c)\,\,2x^2 – 7xy + 5y^2\\=2x^2 – 2xy -5xy + 5y\\=2x(x -y)-5y(x -y)\\=(x-y)(2x-5y)\end{array}$

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