Understanding factoring!?

Question

could someone please explain factoring to me? i have had so many people try and i still dont understand it.

i guess there are four methods you can use.

gcf

difference of 2 squares

testing factors

trinomial square

4x^2 + 5x - 9

y^2 - 9z^2

9x^2 - 16y^2

4y^2 + 36y + 81

y^2 + y - 20

please dont just do the problems. i really really want to understand this. thank you!

Answer 1

∆ = 25 + 144

∆ = 169

x = ( - 5 ± √169 )/8

x = ( - 5 ± 13 )/8

x´= 1

x´´ = - 18/8  =  - 9/4

a.( x - x´).( x - x´´ ) = 0

4.( x - 1 ).( x + 9/4 ) =  0

you  continue... good lucK!!