如何因式分解x^3-1 ?????

x³ - 1
= x³ - x² + x² - x + x - 1
= (x³ - x²) + (x² - x) + (x - 1)
= x²(x - 1) + x(x - 1) + (x - 1)
= (x - 1)(x² + x + 1)

係數和=0,

表示必有x-1的因式,

除完之後就可得到原式=(x-1)(x^2+x+1)

立方差公式 a^3 - b^3 = (a - b)(a^2 + ab + b^2)