Why did I get points off for this answer

I did this on a test:

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

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

x^2(2x + 5) - 4 (2x + 5)

(x^2 - 4)(2x + 5)

I thought I factored it right but I got points off? Help?

The second line should read as -(8x+20). The next step is however correct

And, x^2-4 can be further factorised to (x+2)*(x-2)

So they were probably looking for the answer as: (x+2)(x-2)(2x+5)

First, your 2nd line is wrong

− 8x − 20 = − (8x + 20) -----> NOT − (8x − 20)

Then, you make another mistake going from 2nd to 3rd line

− (8x − 20) = − 4 (2x − 5) -----> NOT − 4 (2x + 5)

But because of mistake you made going from 1st to 2nd line, the mistake going from 2nd to 3rd line actually fixed the first mistake. This is a case of 2 wrongs making a right, but it will get you points taken off. In math, a correct answer arrived at incorrectly does NOT get full points.

Then at the end, you lose more points for not factoring (x^2 − 4) as (x − 2)(x + 2)

Mαthmφm

I am sorry, i am not gonna go through the full answer, as its tedious and time consuming..but I can tell you that right from the second line you have a mistake...
if you factor out a minus from -20 it becomes +20 ..like this >>>> -(8x+20).. that's just the first mistake..
I believe you have to use another factor technique, you can't use this one..i am sure you did it in class or its in your book..

Its the method where you have to find possible factors for a/d(2/-20) or d/a(-20/2) and then see if that number makes the equation zero, then you use long division..
I am positive that if you look, you will find a similar example in your book/lecture notes..

Take care :)

Even though you came up with the correct answer, when you grouped - 8x - 20 inside parentheses in the second step, the sign of - 20 should have changed to + because – outside the parentheses times + inside = – :