因式分解x^3+3px^2+(3p^2-q^2)x+p(p^2-q^2)
问题描述：
因式分解x^3+3px^2+(3p^2-q^2)x+p(p^2-q^2)
用余数定理做
答
x^3+3px^2+(3p^2-q^2)x+p(p^2-q^2)=(x+p)^3-q^2x-pq^2=(x+p)^3-q^2(x+p)=(x+p)[(x+p)^2-q^2]
=(x+p)(x+p+q)(x+p-q)