(x^2+11x+24)(x^2+14x+24)-4x^2 因式分解,详尽点...
1个回答
(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)
