Question

Factorise :- 12x^2 - x - 35 .

Answer 1

Step-1 : Multiply the coefficient of the first term by the constant   12 • -35 = -420 

Step-2 : Find two factors of  -420  whose sum equals the coefficient of the middle term, which is   -1 .

     -420   +   1   =   -419
     -210   +   2   =   -208  
   -140   +   3   =   -137
     -105   +   4   =   -101   
  -84   +   5   =   -79 
    -70   +   6   =   -64  
   -60   +   7   =   -53   
  -42   +   10   =   -32
     -35   +   12   =   -23
     -30   +   14   =   -16 
    -28   +   15   =   -13 
    -21   +   20   =   -1 
  That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -21  and  20 
                     12x2 - 21x + 20x - 35

Step-4 : Add up the first 2 terms, pulling out like factors :
                    3x • (4x-7)
              Add up the last 2 terms, pulling out common factors :
                    5 • (4x-7)
Step-5 : Add up the four terms of step 4 :
                    (3x+5)  •  (4x-7)
             Which is the desired factorization

Final result : (4x - 7) • (3x + 5)

Answer 2

GIven Equation is 12x^2 - x - 35.

                             = 12x^2 - 21x + 20x - 35

                             = 3x(4x - 7) +5(4x - 7)

                             = (3x + 5)(4x - 7).


Hope this helps!