F4 Gmath, 急x100 20pt

1)
f(x)=(x-1)(3x+2)Q(x)+(px+q) , for some polynomial Q(x)
When f(x) is divided by x-1, the remainder is -4
f(1)=4
p+q=4---(1)
when f(x) is divided by 3x+2, the remainder is 6
f(-2/3)=6
-2p/3+q=6---(2)
(1)-(2):
5p/3=-2
p=-6/5 and q=26/5
2)
When f(x) is divided by (x+1)(x-3), the remainder is 2x-4
f(x)=(x+1)(x-3)Q(x)+(2x-4) ,for some polynomial Q(x)
f(3)=3(3)^3+m(3)^2-n(3)-7=2(3)-4
9m-3n=-72
3m-n=-24---(1)
f(-1)=3(-1)^3+m(-1)^2-n(-1)-7=2(-1)-4
m+n=4---(2)
(1)+(2):
4m=-20
m=-5 and n=9

(1) Try to let the ax+b

(2)

(x^2-2x-3)(ax+b)=3x^3+mx^2-nx-7

m=1 , n=9