x^4-10x^3+35x^2-50x+24 和 x^4+x^3-13/2x^2-1/2x+3,用因式定理分解因式,就是

分析,
这样的题,第一步试值,假设x=1,-1,2,-2……,下一步开始分配,
x^4-10x^3+35x^2-50x+24 ,很明显,x=1,和x=2能够使它成了,
∴x^4-10x^3+35x^2-50x+24
=x^4-1-(10x³+10x²)+25(x²-2x+1)
=(x-1)(x³+x²+x+1)-10x²(x-1)+25(x-1)²
=(x-1)(x³-9x²+26x-24)
=(x-1)[x³-2x²-(7x²-26x+24)]
=(x-1)[x²(x-2)-(x-2)(7x-12)]
=(x-1)(x-2)(x²-7x+12)
=(x-1)(x-2)(x-3)(x-4)
下一题,同理,也是先试值,x=2就是它的根,
x^4+x^3-13/2x^2-1/2x+3
=(x-2)(x³+3x²-x/2-3/2)
=(x-2)(x+3)(x+√2/2)(x-√2/2).
【思路就是这样,不懂了,你再问吧.】