Algebra 2 - Precalculus question

So I have to do a review in my Precalculus textbook from Algebra 2 and their are these 2 questions that I just don't seem to understand. I have the answer in the back of the book but I want to know how to get to the answer.

Questions are:

1-8x^2-9x^4 - Answer is -(3x-1)(3x+1)(x^2-1)

(x+2)^2 - 5(x+2) - Answer is - (x+2)(x-3)

3(x^2+10x+25) - 4(x+5) - Answer is (x+5)(3x+11)

I Just don't undestand how they got to those answers.

It's a factoring problem, but I think you wrote the first one down wrong.

-9x^4 - 8x^2 + 1
-1(9(x^2)^2 + 8(x^2) - 1)
-1(9x^2 - 1)(x^2 + 1)
-1(3x + 1)(3x - 1)(x^2 + 1)

(x+2)^2 - 5(x+2)
(x+2)((x+2) - 5) distributive property
(x+2)(x-3) simplify

3(x^2 + 10x + 25) - 4(x+5)
3(x + 5)^2 - 4(x + 5) perfect square
(x+5)(3(x+5) - 4) distributive property
(x+5)(3x + 11) simplify

\omega h\alpha t   th\epsilon   f\mu c\kappa

>>2
has an elegant way but the rational roots theorem works too.

http://www.sosmath.com/algebra/factor/fac10/fac10.html