國中數學因式分解（1）?

21)
When x=-3/2
4(-3/2)^3+k(-3/2)-6=0
-39/2-3k/2=0
-3k/2=39/2
k=-13
4x^3-13x-6=(2x+3)(ax+b)(cx-2)
4x^3-13x-6=[2ax^2+(2a+2b)x+3b](cx-2)
4x^3-13x-6=(2ac)x^3+(2ac+2bc-4a)x^2+(3c-4a-4b)x-6b
-6b=-6
b=1
2ac=4
ac=2
2ac+2c-4a=0
4+2c-4a=0
-4a+2c=-4
-2a+c=-4 i
3c-4a-4=-13
-4a+3c=-9 ii
a=3/2 b=1 c=-1
c/(a-b)
=(-1)/(3/2 -1)
=-2

22)
f(x)=6x^2-7x-1
f(A)=2
6A^2-7A-1=2
A=1.5 or A=-1/3

23)
(1999^2 +3*1999)/(1999^2+4*1999+3)
=1999(1999+3)/[(1999+1)(1999+3)]
=1999/2000

24)
x^2+2bx-(a^2-b^2)
=x^2+2bx+b^2-a^2
=(x+b)^2-a^2
=(x+a+b)(x-a+b)

25)
3(2x-1)^2-10(2x-1)-8
=(2x-1-4)[3(2x-1)+2]
=(2x-5)(6x-1)