SOLUTION: I cant figure out this algebra 2 thing. i just dont understand. could you help me........ Simplify the following expression: 2k2 + 3k - 20 divided by k2 + 3k

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Question 25461: I cant figure out this algebra 2 thing. i just dont understand. could you help me........
Simplify the following expression: 2k2 + 3k - 20 divided by k2 + 3k - 4
Thanks
Answer by josmiceli(19441) (Show Source):
You can put this solution on YOUR website!
It's not easy, but if I can do it, anyone can...sometimes I can't do it either.
take a good hard look at the first one.
There are lots of things to look for.
The highest power is 2. That means it's a quadratic equation.
Maybe it's simple to factor, maybe not
this is the way I factor these things:

what's the simplest factors of the first term?
They are 2k and k because
Now I set up the factors of the equation like this:
(k + _)(2k - _)
Now fill in the blanks
what are the factors of the last term?
2 x 10 = 20
4 x 5 = 20
let's try 2 x 10
(k + 2)( 2k - 10)
each term in the first parenthesis gets multiplied by each term in the second
=

so that's not the answer
Let's swap the 2 and 10
(k + 10)(2k - 2)
=

that's not the answer either
Let's try 4 x 5
(k + 4)(2k - 5)
=

Hey, that's it!
Let's do the other one

the factors of the first term are k and k because
(k + _)(k - _)
fill in the blanks. What are factors of 4?
4 x 1 = 4
2 x 2 = 4
try 4 and 1
(k + 4)(k - 1)

that's it
now back to the original equation
2k2 + 3k - 20 divided by k2 + 3k - 4
substitute the factors for the equations

The (k + 4) factors are on the top and bottom, so they cancel
I end up with

I think that's as simple as I can get it
Don't be afraid of this stuff. The more you do the easier it gets
It doesn't take a genius- just work.

SOLUTION: I cant figure out this algebra 2 thing. i just dont understand. could you help me........ Simplify the following expression: 2k2 + 3k - 20 divided by k2 + 3k - 4 Thanks