College Level Math Practice Test Questions

Need help with questions they are done by hand so please show work or explanation

1 -2x(x+3)-(x+1)(x-2)=
a -x^2-7x-2
b -x^2+5x+2
c -3x^2-7x+2
d -3x^2-5x+2
e -3x^2+5x-2
answer d

2. x/x+2 - 7/x-2=
a x-7/x+2
b x+7/x+2
c x^2-9x-14/x^2-4
d x^2-9x+14/x^2-4
e x-7/4
answer c

For 1. The big idea behind polynomials is grouping them correctly and seeing factors (distribution or factoring).
-2x(x+3)-(x+1)(x-2)
Lets look at this in two parts:
First -2x(x+3)
We can distribute -2x into (x+3)
-2x^2 + (-6x)
Now to our other part: -(x+1)(x-2)
We can solve this by FOIL (First Outer Inner Last)
So... we get x^2 - x - 2
Now we combine our two parts
-2x^2 + (-6x) + -(x^2 - x - 2)
Notice we have to keep the negative sign for the -(x+1)(x-2) and we need to distribute that through.
-2x^2 + (-6x) - x^2 + x + 2)
To make it clear I will group before I simplify
-2x^2 - x^2 - 6x + x + 2
So we get
-3x^2 - 5x +2

For 2. before we doing anything we need a common denominator which in this case is (x+2)(x-2)
Again we will look at it in two pieces:
1. x/x+2 we need an (x-2) here to get that we will multiply by it
x(x-2)/(x+2)(x-2)
2. - 7/x-2 we need an (x+2) here, same process as above
-7(x+2)/(x-2)(x+2)
now we can combine the pieces into one
x(x-2) - 7(x+2) / (x+2)(x-2)
You are pretty much at the same place here as your first problem... distribute and combine like terms.
x(x-2) = x^2 - 2x
- 7(x+2) = -7x - 14
So we get x^2-9x-14
For the bottom we FOIL again
(x+2)(x-2) = x^2 + 2x - 2x - 4 = x^2 - 4
So we get x^2-9x-14 / x^2 - 4
Hope this helps!