(x^2+11x+24)(x^2+14x+24)-4x^2 因式分解,详尽点...

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/06/01 12:08:09

(x^2+11x+24)(x^2+14x+24)-4x^2
=(x^2+12.5x+24-1.5x)(x^2+12.5x+24+1.5x)-4x^2
=(x^2+12.5x+24)²-(1.5x)²-4x^2
=(x^2+12.5x+24)²-2.25x²-4x^2
=(x^2+12.5x+24)²-6.25x²
=(x^2+12.5x+24)²-(2.5x)²
=(x^2+12.5x+24-2.5x)(x^2+12.5x+24+2.5x)
=(x^2+10x+24)(x^2+15x+24)
=(x+4)(x+6)(x^2+15x+24)
有理数范围里分解结束
=(x+4)(x+6)[x^2+15x+(15/2)²-225/4+24]
=(x+4)(x+6)[(x+15/2)²-225/4+96/4]
=(x+4)(x+6)[(x+15/2)²-129/4]
=(x+4)(x+6)(x+15/2+√129/2))(x+15/2-√129/2)
再问：大哥84x^2-271x+195 配方法怎样做
再答： 84x^2-271x+195 =84(x^2-271x/84+195/84) =84[x^2-271x/84+(271/168)²+195/84-73441/28224] =84[x^2-271x/84+(271/168)²+65520/28224-73441/28224] =84[(x-271/168)²-7921/28224] =84[(x-271/168)²-(89/168)²] =84(x-271/168-89/168)(x-271/168+89/168) =84(x-360/168)(x-182/168) =84(x-15/7)(x-13/12) =(7x-15)(12x-13)

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