﹙x³-7x²+4x+12﹚÷﹙x³-4x²-11x-6﹚化简

问题描述:

﹙x³-7x²+4x+12﹚÷﹙x³-4x²-11x-6﹚化简

(x-2)/(x+1)

x³-7x²+4x+12=(x³+x²)-(8x²+8x)+(12x+12)
=x²(x+1)-8x(x+1)+12(x+1)
=(x²-8x+12)(x+1)
=(x-2)(x-6)(x+1)
x³-4x²-11x-6=(x³+x²)-(5x²+5x)-(6x+6)
=x²(x+1)-5x(x+1)-6(x+1)
=(x²-5x-6)(x+1)
=(x+1)²(x-6)
原式=(x-2)/(x+1)