本文利用初等数学知识,以及高等数学中的线性代数知识,结合具体的例题,详尽地论述了实数范围内二元二次多项式ax2+bxy+cy2+dx+ey+f(a2+b2+c2≠0)可分解因式的条件及其分解方法——具体给出实数范围内二元二次多项式ax2+bxy+cy2+dx+ey+f(a2+b2+c2≠0)可分解因式的三个充要条件和一个必要条件,以及六种分解方法。文中同一例题在不同分解方法中的使用,更增添了各种分解方法之间的可比性。 Based on elementary mathematics knowledge and knowledge of linear algebra in higher mathematics, this paper expounds in detail the binary quadratic polynomials ax2 + bxy + cy2 + dx + ey + f (a2 + b2 + c2 ≠ 0) Decomposable factor conditions and their decomposition method - given the real number range of the bivariate quadratic polynomial ax2 + bxy + cy2 + dx + ey + f (a2 + b2 + c2 ≠ 0) Three necessary and sufficient conditions and one necessary condition, and six decomposition methods. The use of the same example in different decomposition methods adds even more comparability among different decomposition methods.