(2008•内江)阅读下列内容后,解答下列各题:几个不等于0的数相乘,积的符号由负因数的个数决定.
例如:考查代数式(x-1)(x-2)的值与0的大小
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,∴(x-1)(x-2)>0
综上:当1<x<2时,(x-1)(x-2)<0
当x<1或x>2时,(x-1)(x-2)>0
(1)填写下表:(用“+”或“-”填入空格处)
(2)由上表可知,当x满足______时,(x+2)(x+1)(x-3)(x-4)<0;
(3)运用你发现的规律,直接写出当x满足______时,(x-7)(x+8)(x-9)<0.
0 169461 169469 169475 169479 169485 169487 169491 169497 169499 169505 169511 169515 169517 169521 169527 169529 169535 169539 169541 169545 169547 169551 169553 169555 169556 169557 169559 169560 169561 169563 169565 169569 169571 169575 169577 169581 169587 169589 169595 169599 169601 169605 169611 169617 169619 169625 169629 169631 169637 169641 169647 169655 366461
例如:考查代数式(x-1)(x-2)的值与0的大小
当x<1时,x-1<0,x-2<0,∴(x-1)(x-2)>0
当1<x<2时,x-1>0,x-2<0,∴(x-1)(x-2)<0
当x>2时,x-1>0,x-2>0,∴(x-1)(x-2)>0
综上:当1<x<2时,(x-1)(x-2)<0
当x<1或x>2时,(x-1)(x-2)>0
(1)填写下表:(用“+”或“-”填入空格处)
(2)由上表可知,当x满足______时,(x+2)(x+1)(x-3)(x-4)<0;
(3)运用你发现的规律,直接写出当x满足______时,(x-7)(x+8)(x-9)<0.
| x<-2 | -2<x<-1 | -1<x<3 | 3<x<4 | x>4 | |
| x+2 | - | + | + | + | + |
| x+1 | - | - | + | + | + |
| x-3 | - | - | - | + | + |
| x-4 | - | - | - | - | + |
| (x+2)(x+1)(x-3)(x-4) | + | - |