文档介绍：一:已知A=(x+2)(x-3)(x+4)(x-5)+49 求证:A为一个完全平方数
A=(x^2-x-6)(x^2-x-20)+49
=(x^2-x)^2-26(x^2-x)+120+49
=(x^2-x)^2-26(x^2-x)+169
=(x^2-x-13)^2
二:x3+5x-6
(x^3-1)+5x-6+1
=(x^3-1)+5x-5
=(x^3-1)+5(x-1)
=(x-1)(x^2+x+1)+5(x-1)
=(x-1)(x^2+x+6)
三:x^2-xy+2x+y-3
=(x^2+2x-3)-(xy-y)
=(x-1)(x+3)-y(x-1)
=(x-1)(x+3-y)
四:x3+9x2+26x+24
=(x3+2x2)+(7x2+14x)+(12x+24)
=x2(x+2)+7x(x+2)+12(x+2)
=(x+2)(x2+7x+12)
=(x+2)(x+3)(x+4).
五、设x4-12x+323=(x2+ax+17)(x2+bx+19),
∴由多项式的乘法得到:x4+(a+b)x3+(36+ab)x2+(19a+17b)x+323=x4-12x+323.
∴a+b=0,
ab+36=0
19a+17b=-12.
∴a=-6,b=6.
∴x4-12x+323
=(x2-6x+17)(x2+6x+19).
六、X2n+Xn-1/9Y2+1/4
=X2n+2*(1/2)Xn+(1/2)2-(1/3Y)2
=[(Xn+(1/2)]2-(1/3Y)2
=[Xn+(1/2)+1/3Y][Xn+(1/2)-1/3Y]
七、