Question

. Phân tích các đa thức sau thành nhân tử:

a) (x² - 1)² - x(x² - 1) - 2x²

b) 4(x² + x + 1)² + 5x(x² + x + 1) + x²

c) (x² - x + 2)⁴ - 3x²(x² - x + 2)² +2x⁴

d) -6(-x² -x + 1)⁴ +7x²(x² -x -1)² +12x⁴

e) 10(x² - 2x + 3)⁴ - 9x²(x² - 2x + 3)² -x⁴

Answer 1

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

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

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

b/ \(=4\left(x^2+x+1\right)^2+4x\left(x^2+x+1\right)+x\left(x^2+x+1\right)+x^2\)

\(=4\left(x^2+x+1\right)\left(x^2+2x+1\right)+x\left(x^2+2x+1\right)\)

\(=\left(x^2+2x+1\right)\left(4x^2+5x+4\right)\)

\(=\left(x+1\right)^2\left(4x^2+5x+4\right)\)

c/ \(=\left(x^2-x+2\right)^4-x^2\left(x^2-x+2\right)^2-2x^2\left(x^2-x+2\right)^2+2x^4\)

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

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

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

Answer 2

d/

Bạn coi lại đề, với hệ số này ko phân tích được

e/

\(=10\left(x^2-2x+3\right)^4-10x^2\left(x^2-2x+3\right)^2+x^2\left(x^2-2x+3\right)^2-x^4\)

\(=10\left(x^2-2x+3\right)^2\left[\left(x^2-2x+3\right)^2-x^2\right]+x^2\left[\left(x^2-2x+3\right)^2-x^2\right]\)

\(=\left[\left(x^2-2x+3\right)^2-x^2\right]\left[10\left(x^2-2x+3\right)^2+x^2\right]\)

\(=\left(x^2-3x+3\right)\left(x^2-x+3\right)\left[10\left(x^2-2x+3\right)^2+x^2\right]\)