因式分解 x四次方-2x³-9x²+2x+8含有因式x²-5x+4,

因式分解 x四次方-2x³-9x²+2x+8含有因式x²-5x+4,
因式分解 x四次方-2x³-9x²+2x+8含有因式x²-5x+4,

因式分解 x四次方-2x³-9x²+2x+8含有因式x²-5x+4,
x⁴- 2x³ - 9x² + 2x + 8
= x⁴- x³ - x³ + x² - 10x² + 10x - 8x + 8
= x³(x-1) - x²(x-1) - 10x(x-1) - 8(x-1)
= (x-1)(x³ - x² - 10x - 8)
= (x-1)(x³ - 4x² + 3x² - 12x + 2x - 8)
= (x-1) { x²(x-4) + 3x(x-4) + 2(x-4) }
= (x-1)(x-4)(x² + 3x + 2)
= (x-1)(x-4)(x² + 2x + x + 2)
= (x-1)(x-4) { x(x+2) + (x + 2) }
= (x-1) (x-4) (x+2) (x+1)
x²-5x+4 可以进一步分解为 (x-1) (x-4)