[Toán 8]Ai giỏi toán giúp tui với!!!!TToTT!!!

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chii123

[TẶNG BẠN] TRỌN BỘ Bí kíp học tốt 08 môn
Chắc suất Đại học top - Giữ chỗ ngay!!

ĐĂNG BÀI NGAY để cùng trao đổi với các thành viên siêu nhiệt tình & dễ thương trên diễn đàn.

Phân tích các đa thức thành nhân tử:
1)[TEX]p^(m+2)q-p^(m+1)q^3-p^2q^(n+1)+pq^(n+2)[/TEX]
2)[TEX]x^2/2+9xy/4-6x/10[/TEX]
3)[TEX]3a^2b^n-27ab^(n+1)[/TEX]
4)[TEX]x^2y^2+y^3+zx^2+yx[/TEX]
5)[TEX](x^2-25)^2-(x-5)^2[/TEX]
6)[TEX](a+b+c)^2+(a+b-c)^2-4c^2[/TEX]
7)[TEX]4b^2c^2-(b^2-c^2-a^2)^2[/TEX]
7)[TEX]x^2-2ax-b^2+a^2[/TEX]
8)[TEX]x^2+6x+5[/TEX]
9)[TEX]x^2-9x+20[/TEX]
10)[TEX]2x^2-6x-2[/TEX]
11)[TEX]3x^2-5x-2[/TEX]
12)[TEX]7x^2+50x+7[/TEX]
13)[TEX]2x^2+x-6[/TEX]
14)[TEX]15x^2+7x-2[/TEX]
15)[TEX]x^2-x-1999*1992[/TEX]
16)[TEX]x^3-2x-4[/TEX]
17)[TEX]x^3+x^2+4[/TEX]
18)[TEX](x^2-8)^2-36[/TEX]
19)[TEX]x^3-19x-30[/TEX]
20)[TEX]x^3-6x^2+11x-6[/TEX]
21)[TEX]6x^3-295x-7[/TEX]
22)[TEX]x^3+2x^2+4x+3[/TEX]
23)[TEX]x^3-3x^2-4x+12[/TEX]
24)[TEX]x^8+x^4+1[/TEX]
25)[TEX]x^8+3x^4+4[/TEX]
26)[TEX]x^7+x^5+1[/TEX]
27)[TEX]x^11+x+1[/TEX]
28)[TEX]a^3+b^3+c^3-3abc[/TEX]
29)[TEX](a+b+c)^3-a^3-b^3-c^3[/TEX]
30)[TEX]x^2(y-z)+y^2(z-x)+z^2(x-y)[/TEX]
31)[TEX](a+1)(a+2)(a+3)(a+4)+1[/TEX]
32)[TEX](a+1)(a+3)(a+5)(a+7)+15[/TEX]
33)[TEX]x^9-x^7-x^6-x^5+x^4+x^3+x^2-1[/TEX]
34)[TEX]x^100+x^99+x^98+...+x^2+x-100[/TEX]
35)[TEX]x^5+x^4-2x+1[/TEX]
36)[TEX](a-b)^3+(b-c)^3+(c-a)^3[/TEX]
37)[TEX]x^8+x+1[/TEX]
38)[TEX]x^4+12x^3+32x^2-8x-4[/TEX]
39)[TEX]3x^4+2x^3-8x^2-2x+5[/TEX]
40)[TEX]2a^2b^2+2b^2c^2+2a^2c^2-a^4-b^4-c^4[/TEX]
 
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C

cuncon2395

chii123 said:
8)[tex]x^2+6x+5[/tex]
9)[tex]x^2-9x+20[/tex]
10)[tex]2x^2-6x-2[/tex]
11)[tex]3x^2-5x-2[/tex]
12)[tex]7x^2+50x+7[/tex]
13)[tex]2x^2+x-6[/tex]
Bấm để xem đầy đủ nội dung ...

. .
8, [TEX]x^2+6x+5=x^2+5x+x+5=x(x+5)+(x+5)=(x+5)(x+1)[/TEX]
9,[TEX]x^2-9x+20=x^2-4x-5x+20=x(x-4)-5(x-4)=(x-4)(x-5)[/TEX]
10, [TEX]2x^2-6x-2=2(x^2-3x+1)[/TEX]
11, [TEX]3x^2-5x-2=3x^2-6x+x-2=3x(x-2)+(x-2)=(x-2)(3x+1)[/TEX]
12, [TEX]7x^2+50x+7=7x^2+49+x+7=7x(x+7)+(x+7)=(x+7)(7x+1)[/TEX]
 
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I

ilovetoan

chii123 said:
Phân tích các đa thức thành nhân tử:
1)[TEX]p^(m+2)q-p^(m+1)q^3-p^2q^(n+1)+pq^(n+2)[/TEX]
2)[TEX]x^2/2+9xy/4-6x/10[/TEX]
3)[TEX]3a^2b^n-27ab^(n+1)[/TEX]
4)[TEX]x^2y^2+y^3+zx^2+yx[/TEX]
5)[TEX](x^2-25)^2-(x-5)^2[/TEX]
6)[TEX](a+b+c)^2+(a+b-c)^2-4c^2[/TEX]
7)[TEX]4b^2c^2-(b^2-c^2-a^2)^2[/TEX]
7)[TEX]x^2-2ax-b^2+a^2[/TEX]
8)[TEX]x^2+6x+5[/TEX]
9)[TEX]x^2-9x+20[/TEX]
10)[TEX]2x^2-6x-2[/TEX]
11)[TEX]3x^2-5x-2[/TEX]
12)[TEX]7x^2+50x+7[/TEX]
13)[TEX]2x^2+x-6[/TEX]
14)[TEX]15x^2+7x-2[/TEX]
15)[TEX]x^2-x-1999*1992[/TEX]
16)[TEX]x^3-2x-4[/TEX]
17)[TEX]x^3+x^2+4[/TEX]
18)[TEX](x^2-8)^2-36[/TEX]
19)[TEX]x^3-19x-30[/TEX]
20)[TEX]x^3-6x^2+11x-6[/TEX]
21)[TEX]6x^3-295x-7[/TEX]
22)[TEX]x^3+2x^2+4x+3[/TEX]
23)[TEX]x^3-3x^2-4x+12[/TEX]
24)[TEX]x^8+x^4+1[/TEX]
25)[TEX]x^8+3x^4+4[/TEX]
26)[TEX]x^7+x^5+1[/TEX]
27)[TEX]x^11+x+1[/TEX]
28)[TEX]a^3+b^3+c^3-3abc[/TEX]
29)[TEX](a+b+c)^3-a^3-b^3-c^3[/TEX]
30)[TEX]x^2(y-z)+y^2(z-x)+z^2(x-y)[/TEX]
31)[TEX](a+1)(a+2)(a+3)(a+4)+1[/TEX]
32)[TEX](a+1)(a+3)(a+5)(a+7)+15[/TEX]
33)[TEX]x^9-x^7-x^6-x^5+x^4+x^3+x^2-1[/TEX]
34)[TEX]x^100+x^99+x^98+...+x^2+x-100[/TEX]
35)[TEX]x^5+x^4-2x+1[/TEX]
36)[TEX](a-b)^3+(b-c)^3+(c-a)^3[/TEX]
37)[TEX]x^8+x+1[/TEX]
38)[TEX]x^4+12x^3+32x^2-8x-4[/TEX]
39)[TEX]3x^4+2x^3-8x^2-2x+5[/TEX]
40)[TEX]2a^2b^2+2b^2c^2+2a^2c^2-a^4-b^4-c^4[/TEX]
Bấm để xem đầy đủ nội dung ...

7/[TEX]x^2-2ax+a^2-b^2[/TEX]
=[TEX](x-a)^2-b^2[/TEX]
=[TEX](x-a-b)(x-a+b)[/TEX]
8/[TEX]x^2+6x+5[/TEX]
=[TEX]x^2+x+5x+5[/TEX]
=[TEX]x(x+1)+5(x+1)[/TEX]
=[TEX](x+1)(x+5)[/TEX]
9/[TEX]x^2-9x+20[/TEX]
=[TEX]x^2-4x-5x+20[/TEX]
=[TEX]x(x-4)-5(x-4)[/TEX]
=[TEX] [B][I][COLOR=#0000ff](x-4)(x-5)[/COLOR][/I][/B][/TEX]
 
C

cuncon2395

chii123 said:
13)[TEX]2x^2+x-6[/TEX]
14)[TEX]15x^2+7x-2[/TEX]
15)[TEX]x^2-x-1999*1992[/TEX]
16)[TEX]x^3-2x-4[/TEX]
17)[TEX]x^3+x^2+4[/TEX]
Bấm để xem đầy đủ nội dung ...

13, [TEX]2x^2+x-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)[/TEX]
14, [TEX]15x^2+7x-2=15x^2-3x+10x-2=3x(5x-1)+2(5x-1)=(5x-1)(3x+2)[/TEX]
16, [TEX]x^3-2x-4=x^3-2x^2+2x^2-4x+2x-4=x^2(x-2)+2x(x-2)+2(x-2)=(x-2)(x^2+2x+2)[/TEX]
17, [TEX]x^3+x^2+4=x^3+2x^2-x^2-2x+2x+4=x^2(x+2)-x(x+2)+2(x+2)=(x+2)(x^2-x+2)[/TEX]
 
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N

nhockhd22

13. 2x^2 +x-6 = 2x^2 - 8 + x+2 = 2(x-2)(x+2) + x+2 = (x+2)(2x-3)

18.(x^2-8)^2 - 36 = (X^2 -8 -6 )(x^2 - 8 +6 ) = (x^2 - 14 )(x^2 -2)

37 x^8 + x+ 1 = (x^8 +x^7 +x^6 ) + (x^5 +X^4 + X^3 ) + (x^2 +x+1 ) - (X^7 +X^6 +X^5 ) - (X^4 + X^3 +x^2 )
=(X^2 +x +1 )(X^6 + X^3 + 1 - X^5 - x^2)
 
C

cuncon2395

chii123 said:
18)[TEX](x^2-8)^2-36[/TEX]
19)[TEX]x^3-19x-30[/TEX]
20)[TEX]x^3-6x^2+11x-6[/TEX]
21)[TEX]6x^3-295x-7[/TEX]
22)[TEX]x^3+2x^2+4x+3[/TEX]
23)[TEX]x^3-3x^2-4x+12[/TEX]
24)[TEX]x^8+x^4+1[/TEX]
Bấm để xem đầy đủ nội dung ...
18)[TEX](x^2-8)^2-36=(x^2-8-6)(x^2-8+6)=(x^2-14)(x^2-2)[/TEX]

19)[TEX]x^3-19x-30=x^3+2x^2-2x^2-4x-15x-30=x^2(x+2)-2x(x+2)-15(x+2)=(x+2)(x^2-2x-15)[/TEX]

20)[TEX]x^3-6x^2+11x-6=x^3-3x^2-3x^2+9x+2x-6=x^2(x-3)-3x(x-3)+2(x-3)=(x-3)(x^2-3x+2)=(x-3)(x-1)(x-2)[/TEX]

21)[TEX]6x^3-295x-7=6x^3+42x^2-42x^2-294x-x-7=6x^2(x+7)-42x(x+7)-(x+7)=(x+7)(6x^2-42x-1)[/TEX]

22)[TEX]x^3+2x^2+4x+3=x^3+x^2+x^2+x+3x+3=x^2(x+1)+x(x+1)+3(x+1)=(x+1)(x^2+x+3)[/TEX]

23)[TEX]x^3-3x^2-4x+12=x^3+2x^2-5x^2-10x+6x+12=x^2(x+2)-5x(x+2)+6(x+2)=(x+2)(x^2-5x+6)=(x+2)(x-3)(x-2)[/TEX]

24)[TEX]x^8+x^4+1=x^4(x^4+1+\frac{1}{x^4})[/TEX]
 
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I

ilovetoan

24/[TEX]x^8+x^4+1=x^8+2x^4+1-x^4=(x^4+1)^2-x^4[/TEX]=

[TEX](x^4-x^2+1)(x^4+x^2+1)=(x^4-x^2+1)(x^2+x+1)(x^2-x+1[/TEX]

25/[TEX]x^8+3x^4+4=(x^4+2)^2-x^4=(x^4-x^2+2)(x^4+2x+2)[/TEX]

26/[TEX]x^7+x^5+1=x^7-x+x^5-x^2+x^2+x+1[/TEX]

=[TEX](x^3-1)[x(x^3+1)+x^2]+x^2+x+1=(x^2+x+1)[x^5-x^4+x^3-x+)[/TEX]
 
L

lunvan

ptdt->nt

13. [TEX]2x^2+-6=2x^2+4x-3x-6=2x(x+2)-3(x+2)=(x+2)(2x-3)[/TEX]
hi, hum trc mình tách nhầm^,^:D
 
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2

251295

chii123 said:
Phân tích các đa thức thành nhân tử:


28)[TEX]a^3+b^3+c^3-3abc[/TEX]
29)[TEX](a+b+c)^3-a^3-b^3-c^3[/TEX]
Bấm để xem đầy đủ nội dung ...




28) [TEX]a^3+b^3+c^3-3abc[/TEX]

[TEX]=(a+b)^3-3ab(a+b)+c^3-3abc[/TEX]

[TEX]=[(a+b)^3+c^3]-3ab(a+b+c)[/TEX]

[TEX]=(a+b+c)[(a+b)^2-(a+b)c+c^2]-3ab(a+b+c)[/TEX]

[TEX]=(a+b+c)[(a+b)^2-(a+b)c+c^2-3ab][/TEX]

[TEX]=(a+b+c)(a^2+2ab+b^2-ac-bc+c^2-3ab)[/TEX]

[TEX]=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)[/TEX]

29) [TEX](a+b+c)^3-a^3-b^3-c^3[/TEX]

[TEX]=[(a+b)+c]^3-a^3-b^3-c^3[/TEX]

[TEX]=(a+b)^3+c^3+3c(a+b)(a+b+c)-a^3-b^3-c^3[/TEX]

[TEX]=a^3+b^3+3ab(a+b)+c^3+3c(a+b)(a+b+c)-a^3-b^3-c^3[/TEX]

[TEX]=3ab(a+b)+3c(a+b)(a+b+c)[/TEX]

[TEX]=3(a+b)[ab+c(a+b+c)][/TEX]

[TEX]=3(a+b)(ab+ac+bc+c^2)[/TEX]

[TEX]=3(a+b)[a(b+c)+c(b+c)][/TEX]

[TEX]=3(a+b)(b+c)(c+a)[/TEX]




 
2

251295

chii123 said:
Phân tích các đa thức thành nhân tử:

30)[TEX]x^2(y-z)+y^2(z-x)+z^2(x-y)[/TEX]
31)[TEX](a+1)(a+2)(a+3)(a+4)+1[/TEX]
32)[TEX](a+1)(a+3)(a+5)(a+7)+15[/TEX]
Bấm để xem đầy đủ nội dung ...



30)[TEX]x^2(y-z)+y^2(z-x)+z^2(x-y)[/TEX]

[TEX]=x^2(y-z)+y^2z-y^2x+z^2x-z^2y[/TEX]

[TEX]=x^2(y-z)+(y^2z-z^2y)-(y^2x-z^2x)[/TEX]

[TEX]=x^2(y-z)+yz(y-z)-x(y-z)(y+z)[/TEX]

[TEX]=(y-z)[x^2+yz-x(y+z)][/TEX]

[TEX]=(y-z)(x^2+yz-xy-xz)[/TEX]

[TEX]=(y-z)[x(x-y)-z(x-y)][/TEX]

[TEX]=(x-y)(y-z)(x-z)[/TEX]

31)[TEX](a+1)(a+2)(a+3)(a+4)+1[/TEX]

[TEX]=(a^2+5a+4)(a^2+5a+6)+1[/TEX]

[TEX]=[(a^2+5a+5)-1][(a^2+5a+5)+1]+1[/TEX]

[TEX]=(a^2+5a+5)^2-1+1[/TEX]

[TEX]=(a^2+5a+5)^2[/TEX]

32)[TEX](a+1)(a+3)(a+5)(a+7)+15[/TEX]

[TEX]=(a^2+8a+7)(a^2+8a+15)+15[/TEX]

[TEX]=[(a^2+8a+11)-4][(a^2+8a+11)+4]+15[/TEX]

[TEX]=(a^2+8a+11)^2-16+15[/TEX]

[TEX]=(a^2+8a+11)^2-1[/TEX]

[TEX]=(a^2+8a+11-1)(a^2+8a+11+1)[/TEX]

[TEX]=(a^2+8a+10)(a^2+8a+12)[/TEX]


 
T

thienthanlove20

8)[TEX]x^2 + 6x + 5[/TEX]

[TEX] = x^2 + 5x + x + 5[/TEX]

[TEX] = x(x + 5) + (x + 5)[/TEX]

[TEX] = (x + 5)(x + 1)[/TEX]

9)[TEX]x^2 - 9x + 20[/TEX]

[TEX]= x^2 - 5x - 4x + 20[/TEX]

[TEX] = x(x - 5) - 4(x - 5)[/TEX]

[TEX]= (x - 5)(x - 4)[/TEX]

11)[TEX]3x^2 - 5x - 2[/TEX]

[TEX] = 3x^2 - 6x + x - 2[/TEX]

[TEX] = 3x(x - 2) + (x - 2)[/TEX]

[TEX] = (x - 2)(3x + 1)[/TEX]

12)[TEX]7x^2+50x+7[/TEX]

[TEX] = 7x^2 + 49x + x + 7[/TEX]

[TEX] = 7x(x + 7) + (x + 7)[/TEX]

[TEX] = (x + 7)(7x + 1)[/TEX]

13)[TEX]2x^2 + x - 6[/TEX]

[TEX] = 2x^2 + 4x - 3x - 6[/TEX]

[TEX] = 2x(x + 2) - 3(x + 2)[/TEX]

[TEX] = (x + 2)(2x - 3)[/TEX]

14)[TEX]15x^2 + 7x - 2[/TEX]

[TEX] = 15x^2 + 10x - 3x - 2[/TEX]

[TEX] = 15x(x + 2/3) - 3(x + 2/3)[/TEX]

[TEX] = (x + 2/3)(15x - 3)[/TEX]

16)[TEX]x^3 - 2x - 4[/TEX]

[TEX] = x^3 - 2x^2 + 2x^2 - 4x + 2x - 4[/TEX]

[TEX] = x^2(x - 2) + 2x(x - 2) + 2(x - 2)[/TEX]

[TEX] = (x - 2)(x^2 + 2x + 2)[/TEX]

17)[TEX]x^3+x^2+4[/TEX]

[TEX] = x^3 + 2x^2 - x^2 - 2x + 2x + 4[/TEX]

[TEX] = x^2(x + 2) - x(x + 2) + 2(x + 2)[/TEX]

[TEX] = (x + 2)(x^2 - x + 2)[/TEX]
 
T

thienthanlove20

37.Ta có:

[TEX]x^8 + x + 1 = x^8 + x^4 - x^4 + x^2 - x^2 + x + 1[/TEX]

[TEX] = (x^8 + x^4 + 1) - (x^4 + x^2 + 1) + (x^2 + x + 1)[/TEX]...........(1)

trong đó:

[TEX]x^4 + x^2 + 1 = x^4 + 2x^2 - x^2 + 1 = (x^4 + 2x^3 + 1) - x^2 = (x^2 + 1)^2 - x^2[/TEX]

[TEX] = (x^2 + 1 - x)(x^2 + 1 + x)[/TEX]

[TEX] = (x^2 - x + 1)(x^2 + x + 1)[/TEX]...............(2)

[TEX]x^8 + x^4 + 1 = x^8 + 2x^4 - x^4 + 1 = (x^8 + 2x^4 + 1) - x^4[/TEX]

[TEX] = (x^4 + 1)^2 - (x^2)^2 = (x^4 + 1 - x62)(x^4 + 1 + x^2)[/TEX]

[TEX] = 9x^4 - x62 + 1)(x^4 + x^2 + 1)[/TEX]

[TEX] = (x^4 - x^2 + 1)(x^2 - x + 1)(x^2 + x + 1)[/TEX]............(3)

Thay (2), (3) vào (1) ta đc:

[TEX]x^8 + x + 1 = (x^4 - x^2 + 1)(x^2 - x + 1)(x^2 + x + 1) - (x^2 - x + 1)(x^2 + x + 1) + (x^2 + x + 1)[/TEX]

[TEX] = (x^2 + x + 1)[(x^4 - x^2 + 1)(x^2 - x + 1) - (x^2 - x + 1) + 1][/TEX]

[TEX] = (x^2 + x + 1)(x^6 - x^5 + x^3 - x^2 + 1)[/TEX]
 
T

thienthanlove20

33)[TEX]x^9-x^7-x^6-x^5+x^4+x^3+x^2-1[/TEX]
[TEX] = x^7(x - 1)(x + 1) - x^5(x + 1) + x^3(x + 1) + (x - 1)(x + 1)[/TEX]
[TEX] = (x + 1)(x^8 - x^7 - x^5 + x^3 + x - 1)[/TEX]
[TEX] = (x + 1)(x - 1)(x^7 - x^5 - x^3 + 1)[/TEX]
[TEX] = (x + 1)(x - 1)^2(x^2 + 2x + 2)[/TEX]
 
C

cuncon2395

39)[TEX]3x^4+2x^3-8x^2-2x+5[/TEX]
[TEX]=3x^4-3x^3+5x^3-5x^2-3x^2+3x-5x+5[/TEX]
[TEX]=3x^3(x-1)+5x^2(x-1)-3x(x-1)-5(x-1)[/TEX]
[TEX]=(x-1)(3x^3+5x^2-3x-5)[/TEX]
[TEX]=(x-1)[3x(x^2-1)+5(x^2-1)][/TEX]
[TEX]=(x-1)(x^2-1)(3x+5)[/TEX]
[TEX]=(x-1)^2(x+1)(3x+5)[/TEX]

5, [TEX](x^2-25)^2-(x-5)^2=(x^2-25-x+5)(x^2-25+x-5)=(x^2-x-20)(x^2+x-30)=(x+4)(x-5)(x-5)(x+6)[/TEX]
 
T

thienthanlove20

5)[TEX](x^2-25)^2-(x-5)^2[/TEX]

[TEX] = (x - 5)^2(x + 5)^2 - (x - 5)^2[/TEX]
[TEX] = (x - 5)^2(x^2 + 10x +25 - 1)[/TEX]
[TEX] = (x - 5)^2(x^2 + 10x + 24)[/TEX]
[TEX] = (x - 5)^2(x + 4)(x + 6)[/TEX]
 
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