國中三的數學問題(希望是有步驟的)10points!!

Question

1、那一個是
x^(4)-x^(3)-x+1 的因子 (Factor)?

2、因式分解 (24x^3)-375.

3、簡化 (6x+18y)/[2(x^2)y+6xy^2].

4、因式分解 (a+b)(c+d)+(a+b)[(c^2)+(d^2)]

5、因式分解 {[36x+23]^2 } -1

6、因式分解 [(49a^2)/36] + [36 / (49a^2)]

7、因式分解以下題目":
a. -10(x^2)+x+3
b. (16x^2)-2x-3
c. 5(x^2) + 19x +18


d. 4(m^4)
e. 9 [ (1/m^2) + m + m^2]
f. 108m^2 + 147
g. [(m^2)+1 / m ] [(1-m^2) / m]

h. (n^4 - 1) / (n^3 + n^2 + n + 1)

i. 根據以下 9a^2 - 6a + 1, 分解 (9x^2 - 18xy + 9y^2) - 6x +6y +1


j. a^2 - 9b^2 = 36, (a/3) + b = 6.
a-3b= ??

k. [2/ (x^2 + 4x +3 )] + [1/ (x^2 + 7x +12)]


完..

Answer 1

1.x4-x3-x+1=x3(x-1)-(x-1)=(x-1)(x3-1)=(x-1)(x-1)(x2+x+1)2.24x3-375=3(8x3-125)=3[(2x)3-53]=3(2x-5)(4x2+10x+25)3.(6x+18y)/[2(x2)y+6xy2]=6(x+3y)/2xy(x+3y)=3/xy4.(a+b)(c+d)+(a+b)(c2+d2)=(a+b)(c2+c+d2+d)5.(36x+23)2-1=(36x+23+1)(36x+23-1)=(36x+24)(36x+22)=24(3x+2)(18x+11)6.[(49a2)/36] + [36 / (49a2)]=[(49a2)2+(36)2]/36*49a2=(2401a4+1296)/1764a2

2006-10-25 19:37:21 補充：
a. -10(x^2)+x+3=(2x+1)(-5x+3)b.(16x^2)-2x-3=(2x-1)(8x+3)c.5(x^2) + 19x +18=(x+2)(5x+9)

2006-10-25 20:47:57 補充：
d. 4(m^4)e. 9 [ (1/m^2) + m + m^2]f. 108m^2 + 147=3(36m^2+49)=3[(6m)^2+(7)^2]g. [(m^2)+1 / m ] [(1-m^2) / m]=[(1-m+m^2)(1-m)(1+m^2)]/m^2

2006-10-25 20:51:18 補充：
h. (n^4 - 1) / (n^3 + n^2 + n + 1)=(n^2+1)(n^2-1)/n^2(n+1)+(n+1)=(n^2+1)(n+1)(n-1)/(n^2+1)(n+1)=(n-1)

2006-10-25 20:54:38 補充：
i. (9x^2 - 18xy + 9y^2) - 6x +6y +1=9(x-y)^2-6(x-y)+1=[3(x-y)-1]^2=(3x-3y-1)^2

2006-10-25 20:57:40 補充：
j.(a/3) + b = 6→a+3b=18a^2 - 9b^2 = 36→(a+3b)(a-3b)=36→a-3b=2

2006-10-25 21:00:46 補充：
k. [2/ (x^2 + 4x +3 )] + [1/ (x^2 + 7x +12)]=[2/(x+3)(x+1)] + [1/(x+3)(x+4)]=[2(x+4)+(x+1)]/(x+1)(x+3)(x+4)=3/(x+1)(x+4)