Why did I get points off for this answer

I see where you screwed up, 2nd line going to the third line.

(2x^3+5x^2)-(8x-20)
You did something weird with the negative sign and the 4 that you factored out and the 5.

The third line should be
x^2(2x+5)-4(2x-5)

Please notice the negative sign in front of the five.

2x^3 + 5x^2 - 8x - 20

(2x^3 + 5x^2) - (8x - 20)
................... ↑ when you factored out the negative, you forgot to make the 20 positive

(2x^3 + 5x^2) - (8x + 20 )

It is factored right however one more step is needed (x^2 - 4) can break down into (x+2)(x-2)

Thus the complete answer is (x+2)(x-2)(2x + 5)

Perfect as far as it goes, but you forgot (and this is common) that x^2 - 4 is a difference of squares and can be factored further into (x - 2)( x+ 2)

The second line looks wrong. Should be: (2x^3 + 5x^2) - (8x + 20)

Notice the + before 20.

In the 3rd step, when you took 4 out, you changed the sign inside the bracket. There was a minus sign outside already. You took out 4. Not -4.

You didn't finish the job - - (x^2 - 4) = (x+2)(x-2)

(x^2 - 4)
=(x-2)(x+2)

(x+2)(x-2)(2x+5)

it ll be...

(2x^3 + 5x^2 ) - ( 8x + 20 )

Ask your teacher to explain it. He or she must have a reasonable answer.

I'm never going to visit this part of Yahoo!® ANSWERS again.