Question

(6x^2-7x-5)÷(2x+1) please help

Answer 1

...... this is a solution

Answer 2

Step  1  :

Equation at the end of step  1  :

Step  2  :

6x2 - 7x - 5/ 2x - 1 simplify

Trying to factor by splitting the middle term

 2.1     Factoring  6x2 - 7x - 5 

The first term is,  6x2  its coefficient is  6 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  -5 

Step-1 : Multiply the coefficient of the first term by the constant   6 • -5 = -30 

Step-2 : Find two factors of  -30  whose sum equals the coefficient of the middle term, which is   -7 .

  -30   +   1   =   -29   
  -15   +   2   =   -13   
  -10   +   3   =   -7  
 That's it


Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -10  and  3 
                     6x2 - 10x + 3x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
                    2x • (3x-5)
              Add up the last 2 terms, pulling out common factors :
                     1 • (3x-5)
Step-5 : Add up the four terms of step 4 :
                    (2x+1)  •  (3x-5)
             Which is the desired factorization

Final result :

(3x - 5) • (2x + 1) / 2x - 1