is the answer to this algebra problem correct?

Question

2x squared + x - 6 over 2x + 4 equals a - 2b

if it's wrong, how do i solve it correctly?

AND

how would you solve 2x squared - 32 over x - 4? why doesnt it equal 2x - 8?

Answer 1

I'm not sure what you meant with the first one, but:
(2X^2 + x -6) / (2x +4)

Factor out a two on bottom and since
(2x - 3)(x+2) = 2x^2 + x - 6 then

(2x-3)(x+2) / 2(x+2)

the (x+2) cancels so

(2x-3)/ 2 = x-3/2




The answer to the second one goes like this:

(2x^2 - 32)/(x-4)

Factor out the two on top
2(x^2 - 16) / (x-4)

Now factor
(x-4)(x+4) = x^2 -4x +4x -16, so

2(x-4)(x+4) / (x-4)

the (x-4) cancels out so

2(x+4) / 1 = 2(x + 4) = 2x +8

Answer 2

Not sure how you got a - 2b on that first one. Maybe I'm thinking of it differently. I got x-3/2 for the answer to the first one... You can do long division to get that answer. (Excuse the funky format, please, it spaces refused to work for me...)
.........._x___-3/2__
2x+4./.2x^2+x..-6
...........2x^2-4x
..................-3x-6
...................3x+6 = 0 remainder

As for the second one... x-4 doesn't go into 2x^2-32 equally, it would have a remainder... You can show this with long division again.
........._2x____8___
x - 4 / 2x^2.........-32
.........-2x^2+8x
....................8x - 32
...................-8x+32 = 0
You just got the sign wrong on that last one... You can also check if it's the answer or not by multiplying it out.
(2x-8)(x-4) = 2x^2 - 8x - 8x + 32 = 2x^2 - 16x + 32

That doesn't equal out to your original amount (2x^2 - 32)

Answer 3

(2x-3)(x+2)
------------- =2x-3/2------ answer
2(x+2)
2(x^2-16) 2(x-4)(x+4)
---------------------------- 2(x+4)---- answer
x-4 x-4