因式分解x^3+3px^2+(3p^2-q^2)x+p(p^2-q^2)用余数定理做_数学解答

因式分解x^3+3px^2+(3p^2-q^2)x+p(p^2-q^2)
用余数定理做

人气：467 ℃　时间：2020-09-21 15:21:05

解答

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)