Question

Đề bài: Phân tích đa thức thành nhân tử:

a) x^ 4- 4x^3+ 8x + 3.

b) x^2 (y^2 - 4)^2 - 6x(y^2 - 4) + 9.

c) a^4 - 9a^3 + 81a^2 - 81

Answer 1

a) \(x^4-4x^{3^{ }}+8x+3\)

\(=\left(x^4+x^3\right)-\left(5x^3+5x^2\right)+\left(5x^2+5x\right)+\left(3x+3\right)\)

\(=x^{3^{ }}\left(x+1\right)-5x^{2^{ }}\left(x+1\right)+5x\left(x+1\right)+3\left(x+1\right)\)

\(=\left(x+1\right)\left(x^3-5x^2+5x+3\right)\)

\(=\left(x+1\right)\left[\left(x^3-3x^2\right)-\left(2x^2-6x\right)-\left(x-3\right)\right]\)

\(=\left(x+1\right)\left[x^2\left(x-3\right)-2x\left(x-3\right)-\left(x-3\right)\right]\)

\(=\left(x+1\right)\left(x-3\right)\left(x^2-2x-1\right)\)

\(=\left(x+1\right)\left(x-3\right)\left[\left(x-1\right)^2-2\right]\)

\(=\left(x+1\right)\left(x-3\right)\left(x-1-\sqrt{2}\right)\left(x-1+\sqrt{2}\right)\)

Answer 2

b, \(x^2\left(y^2-4\right)^2-6x\left(y^2-4\right)+9\)

\(=\left[x\left(y^2-4\right)-3\right]^2\)

\(=\left(xy^2-4x-3\right)^2\)