【解析】(1)Solution:Using the splitting the middle term method,We have to find a number whose sum=-7 andproduct=1×12=12We get -3 and -4 as the numbers [-3+-4=-7and -3×-4=12]12x2-7x+1=12x2-4x-3x+1=4x (3x-1)-1(3x-1)=(4x-1)(3x-1)(2)Solution:Usi...
(i) x3+3x2+3x−7=(x+1)3−23a3−b3=(a−b)(a2+ab+b2)=(x+1−2){(x+1)2+(x+1)2+22}=(x−1){(x2+12+2x+2x+2)+4}=(x−1)(x2+4x+7)∴x3+3x2+3x−7=(x−1)(x2+4x+7)(ii) x3−3x2+3x+7=x3−4x2+x2+7x−4x+7=(x3−4x2+7x)+1(x2...
⑴法一:原式=x4+2x3+3x2+2x+1=x4+2x3+x2+2x2+2x+1=(x2+x)2+2(x2+x)+1=(x2+x+1)2;法二:原式=(x4+1)+2x(x2+1)+3x2=(x2+1)2−2x2+2x(x2+1)+3x2=(x2+1)2+2x(x2+1)+x2=(x2+x+1)2.⑵原式=(x4+1)+7x(x2+1)+14x2=(x2+1)2+7x(x2+...