Anyone good at math????

I am prepping for a college placement test tomorrow and its been several years since I took or even looked at math and I am stuck on figuring out how to work a few problems. I have the questions and answers but no idea how to get from point A to point B. Please explain. Thanks

Reduce to lowest terms:

2x^2-3x-2
------------- (divided by)
10+x-3x^2

Answer: -2x-1
--------------
10+x-3x^2

When x^3+3x^2-2 is divided by x+1, the remainder is:
Answer: 11

the numerator
2x^2-3x-2

quadratic formula
the discriminant
+/-sqrt(b^2-4ac)
9+16
25
+/-5

rest of q.f.
(-b+/-5)/2a
(3+/-5)/4

8/4, -2/4
2, -1/2

extract the factors
x=2
x-2=0
(x-2)

x= -1/2
2x= -1
2x+1=0
(2x+1)

the denominator
10+x-3x^2

you can solve this the way it is written

the discriminant
+/-sqrt(b^2-4ac)
1+120
121
+/-11

rest of q.f.
(-b+/-11)/2a
(-1+/-11)/20
10/20, -12/20
1/2, -3/5

extract the multiples
x= 1/2
2x=1
(2x-1)

x= -3/5
5x= -3
(5x+3)

except........
the 'x' is in the other position
(2-x) = (-x+2)= -(x-2)
[thats the trick here]
and
(5+3x)=(3x+5)

all together
(x-2)(2x+1) / -(x-2)(3x+5)

(x-2)/(x-2) cancels
leaving
-(2x+1)/(3x+5)


for the second one
there is a shortcut
[good news after the long winded first answer, eh?]

divided by (x+1)
which means
x= -1

substitute -1 for x in the equation
x^3+3x^2-2
-1+3-2
0

(x+1) is a factor

oh well

long division

divide the 'x' from x+1 into the leading term
see what the +1 generates
subtract

x^3/x=x^2
x^2(x+1)=x^3+x^2

subtract
2x^2-2

2x^2/x=2x
2x(x+1)=2x^2+2x

subtract from 2x^2-2
-2x-2

hope you can see
(-2x-2)/(x+1)= -2