Đáp án:
`a)(x²+x-5)(x²+x+3)`
`b)(x²-8x+17)(x²-8x+5)`
`c)x(x²+5x+10)(x+5)`
`d)(x+2)(x+4)(x²+5x+8)`
`e)(x²-3x-8)(x²-6x-8)`
Giải thích các bước giải:
`a)(x^2+x)^2-2(x^2+x)-15`
Đặt `x²+x=a` ,khi đó ta được:
`a²-2a-15`
`=a²-5a+3a-15`
`=a(a-5)+3(a-5)`
`=(a-5)(a+3)`
`=(x²+x-5)(x²+x+3)`
`b)(x-1)(x-3)(x-5)(x-7)-20`
`=[(x-1)(x-7)][(x-3)(x-5)]-20`
`=(x²-7x-x+7)(x²-5x-3x+15)-20`
`=(x²-8x+7)(x²-8x+15)-20`
Đặt `x²-8x+11=a` ,khi đó ta được:
`(a-4)(a+4)-20`
`=a²-4²-20`
`=a²-16-20`
`=a²-36`
`=a²-6²`
`=(a+6)(a-6)`
`=(x²-8x+11+6)(x²-8x+11-6)`
`=(x²-8x+17)(x²-8x+5)`
`c)(x+1)(x+2)(x+3)(x+4)-24`
`=[(x+1)(x+4)][(x+2)(x+3)]-24`
`=(x²+4x+x+4)(x²+3x+2x+6)-24`
`=(x²+5x+4)(x²+5x+6)-24`
Đặt `x²+5x+5=a` ,khi đó ta được:
`(a-1)(a+1)-24`
`=a²-1-24`
`=a²-25`
`=a²-5²`
`=(a+5)(a-5)`
`=(x²+5x+5+5)(x²+5x+5-5)`
`=(x²+5x+10)(x²+5x)`
`=x(x²+5x+10)(x+5)`
`d)(x^2+4x+8)^2+3x(x^2+4x+8)+2x²`
Đặt `x²+4x+8=a` ,khi đó ta được:
`a²+3ax+2x²`
`=a²+2ax+ax+2x²`
`=a(a+2x)+x(a+2x)`
`=(a+2x)(a+x)`
`=(x²+4x+8+2x)(x²+4x+8+x)`
`=(x²+6x+8)(x²+5x+8)`
`=(x²+2x+4x+8)(x²+5x+8)`
`=[x(x+2)+4(x+2)](x²+5x+8)`
`=(x+2)(x+4)(x²+5x+8)`
`e)(x+1)(x-4)(x+2)(x-8)+4x²`
`=[(x+1)(x-8)][(x-4)(x+2)]+4x²`
`=(x²-8x+x-8)(x²+2x-4x-8)+4x²`
`=(x²-7x-8)(x²-2x-8)+4x²`
Đặt `x²-7x-8=a` ,khi đó ta được:
`a(a+5x)+4x²`
`=a²+5ax+4x²`
`=a²+4ax+ax+4x²`
`=a(a+4x)+x(a+4x)`
`=(a+4x)(a+x)`
`=(x²-7x-8+4x)(x²-7x-8+x)`
`=(x²-3x-8)(x²-6x-8)`
