Question

Factorise 5-4x(1+3x)

Answer 1

We have to factorize ...   5 - 4 x ( 1 + 3 x)

       5 - 4 x - 12 x²
    = - [ 12 x² + 4 x - 5 ]
   12 * -5 = -60.  Find the factors of -60 such that difference/sum is 4.
      -60 = -5 * 12,  10 * - 6 

  So  - [ 12 x² + 10 x - 6 x - 5 ]
        - [  2 x ( 6x + 5)  - 1 (6 x + 5) ]
        - [ (2 x -1) (6x+5) ]
     = - (2x -1) (6x+5)
answer.

Answer 2

5-4x(1+3x)
5-4x-12x² =0
12x²+4x-5 = 0

Apply D = b²-4ac
we get D = 4²-4×12×(-5)
= 16+240 = 256
Now roots are
= -b ±√D/2a
plug in the values we get :-
= -4±16/2(12)
thus two roots are 1/2 and -5/6
hence factors are (x-1/2) & (x+5/6)