求以下數學題答案 (要有過程)

1.If x-3 is a common factor of f(x)=x^3+mx^2+nx+6 and g(x)=2x^3+nx^2+2mx+3 where m and n are contants. Find the values of m and n.f(3)=27+9m+3n+6=0 => 3m+n+11=0g(3)=54+9n+6m+3=0 => 2m+3n+19=0Use Cramer's rule to find m & n:|3,1,11,3|
|2,3,19,2|=[9-2,19-33,22-57]=[7,-14,-35]m=-14/7=-2, n=-35/7=-3ans=(m,n)=(-2,-3)
2.If f(x)=x^3-(k-1)x^2+x-6 is divisible by x-k where k is a contant. Find the values of k.f(k)=k^3-k^2(k-1)+k-6=0 => k^2+k-6=0(k+3)(k-2)=0 => k=2,-3.......ans
3.Simplify each of the following: w=1/(3x-6)+2/(x+2)-2x/(3x^2-12) w=1/3(x-2)+2/(x+2)-2x/3(x^2-4)=[(x+2)+6(x-2)-2x]/[3(x^2-4)]=(x+2+6x-12-2x)/[3(x^2-4)]=(5x-10)/3(x^2-4)=5(x-2)/3(x^2-4)=5/3(x+2)...........ans
4.2x+1 is a factor of the polynomial f(x)=mx^3+nx^2+3x-1 where m and n are constants. f(x) is divided by x-2, the remainder is 33(a) find the values of m and nf(-1/2)=-m/8+n/4-3/2-1=0 => m-2n+20=0f(2)=8m+4n+6-1=33 => 2m+n-7=0Use Cramer's rule to find m & n:|1,-2,20,1|
|2,.1,-7,2|=[1+4,14-20,40+7]=[5,-6,47]m=-6/5, n=47/5........ans
(b) factorize f(x) into factors with intergral coefficientsf(x)=-6x^3/5+47x^2/5+3x-1=(-6x^3+47x^2+15x-5)/5(c) hence,find the real root(s) of the equation f(x)=00=6x^3-47x^2-15x+5=(2x+1)(3x^2-25x+5)x=-1/2 or x=[25+-√(625-60)]/6=(25+-√565)/6
5.If (kx+1)/(x^2+x-2)-1/(x+2)=1/(x+1) where k is a constant.Find the values of k.(kx+1)/(x-1)(x+2)=1/(x+2)+1/(x+1)=(x+1+x+2)/(x+2)(x+1)(kx+1)/(x-1)=(2x+3)/(x+1); x=\=-2(kx+1)(x+1)=(x-1)(2x+3) => kx^2+kx+x+1=2x^2+3x-2x-3kx^2+kx=2x^2-4 => k=2.........ans

In the answer of 麻辣：
n = -35/7 = -5 (but NOT -3)